diff --git a/include/qemu/accel.h b/include/qemu/accel.h
index be56da1b99..ce4747634a 100644
--- a/include/qemu/accel.h
+++ b/include/qemu/accel.h
@@ -43,6 +43,10 @@ typedef struct AccelClass {
     bool (*has_memory)(MachineState *ms, AddressSpace *as,
                        hwaddr start_addr, hwaddr size);
 #endif
+
+    /* gdbstub related hooks */
+    int (*gdbstub_supported_sstep_flags)(void);
+
     bool *allowed;
     /*
      * Array of global properties that would be applied when specific
@@ -92,4 +96,12 @@ void accel_cpu_instance_init(CPUState *cpu);
  */
 bool accel_cpu_realizefn(CPUState *cpu, Error **errp);
 
+/**
+ * accel_supported_gdbstub_sstep_flags:
+ *
+ * Returns the supported single step modes for the configured
+ * accelerator.
+ */
+int accel_supported_gdbstub_sstep_flags(void);
+
 #endif /* QEMU_ACCEL_H */
diff --git a/include/sysemu/kvm.h b/include/sysemu/kvm.h
index efd6dee818..a20ad51aad 100644
--- a/include/sysemu/kvm.h
+++ b/include/sysemu/kvm.h
@@ -47,7 +47,6 @@ extern bool kvm_direct_msi_allowed;
 extern bool kvm_ioeventfd_any_length_allowed;
 extern bool kvm_msi_use_devid;
 extern bool kvm_has_guest_debug;
-extern int kvm_sstep_flags;
 
 #define kvm_enabled()           (kvm_allowed)
 /**
@@ -174,12 +173,6 @@ extern int kvm_sstep_flags;
  */
 #define kvm_supports_guest_debug() (kvm_has_guest_debug)
 
-/*
- * kvm_supported_sstep_flags
- * Returns: SSTEP_* flags that KVM supports for guest debug
- */
-#define kvm_get_supported_sstep_flags() (kvm_sstep_flags)
-
 #else
 
 #define kvm_enabled()           (0)
@@ -198,7 +191,6 @@ extern int kvm_sstep_flags;
 #define kvm_ioeventfd_any_length_enabled() (false)
 #define kvm_msi_devid_required() (false)
 #define kvm_supports_guest_debug() (false)
-#define kvm_get_supported_sstep_flags() (0)
 
 #endif  /* CONFIG_KVM_IS_POSSIBLE */
 
diff --git a/accel/accel-common.c b/accel/accel-common.c
index 50035bda55..df72cc989a 100644
--- a/accel/accel-common.c
+++ b/accel/accel-common.c
@@ -129,6 +129,16 @@ bool accel_cpu_realizefn(CPUState *cpu, Error **errp)
     return true;
 }
 
+int accel_supported_gdbstub_sstep_flags(void)
+{
+    AccelState *accel = current_accel();
+    AccelClass *acc = ACCEL_GET_CLASS(accel);
+    if (acc->gdbstub_supported_sstep_flags) {
+        return acc->gdbstub_supported_sstep_flags();
+    }
+    return 0;
+}
+
 static const TypeInfo accel_cpu_type = {
     .name = TYPE_ACCEL_CPU,
     .parent = TYPE_OBJECT,
diff --git a/accel/kvm/kvm-all.c b/accel/kvm/kvm-all.c
index 5acab1767f..c55938453a 100644
--- a/accel/kvm/kvm-all.c
+++ b/accel/kvm/kvm-all.c
@@ -175,7 +175,7 @@ bool kvm_direct_msi_allowed;
 bool kvm_ioeventfd_any_length_allowed;
 bool kvm_msi_use_devid;
 bool kvm_has_guest_debug;
-int kvm_sstep_flags;
+static int kvm_sstep_flags;
 static bool kvm_immediate_exit;
 static hwaddr kvm_max_slot_size = ~0;
 
@@ -3712,6 +3712,17 @@ static void kvm_accel_instance_init(Object *obj)
     s->kvm_dirty_ring_size = 0;
 }
 
+/**
+ * kvm_gdbstub_sstep_flags():
+ *
+ * Returns: SSTEP_* flags that KVM supports for guest debug. The
+ * support is probed during kvm_init()
+ */
+static int kvm_gdbstub_sstep_flags(void)
+{
+    return kvm_sstep_flags;
+}
+
 static void kvm_accel_class_init(ObjectClass *oc, void *data)
 {
     AccelClass *ac = ACCEL_CLASS(oc);
@@ -3719,6 +3730,7 @@ static void kvm_accel_class_init(ObjectClass *oc, void *data)
     ac->init_machine = kvm_init;
     ac->has_memory = kvm_accel_has_memory;
     ac->allowed = &kvm_allowed;
+    ac->gdbstub_supported_sstep_flags = kvm_gdbstub_sstep_flags;
 
     object_class_property_add(oc, "kernel-irqchip", "on|off|split",
         NULL, kvm_set_kernel_irqchip,
diff --git a/accel/tcg/tcg-all.c b/accel/tcg/tcg-all.c
index 47952eecd7..30b503fb22 100644
--- a/accel/tcg/tcg-all.c
+++ b/accel/tcg/tcg-all.c
@@ -25,6 +25,7 @@
 
 #include "qemu/osdep.h"
 #include "sysemu/tcg.h"
+#include "sysemu/replay.h"
 #include "sysemu/cpu-timers.h"
 #include "tcg/tcg.h"
 #include "qapi/error.h"
@@ -207,12 +208,28 @@ static void tcg_set_splitwx(Object *obj, bool value, Error **errp)
     s->splitwx_enabled = value;
 }
 
+static int tcg_gdbstub_supported_sstep_flags(void)
+{
+    /*
+     * In replay mode all events will come from the log and can't be
+     * suppressed otherwise we would break determinism. However as those
+     * events are tied to the number of executed instructions we won't see
+     * them occurring every time we single step.
+     */
+    if (replay_mode != REPLAY_MODE_NONE) {
+        return SSTEP_ENABLE;
+    } else {
+        return SSTEP_ENABLE | SSTEP_NOIRQ | SSTEP_NOTIMER;
+    }
+}
+
 static void tcg_accel_class_init(ObjectClass *oc, void *data)
 {
     AccelClass *ac = ACCEL_CLASS(oc);
     ac->name = "tcg";
     ac->init_machine = tcg_init_machine;
     ac->allowed = &tcg_allowed;
+    ac->gdbstub_supported_sstep_flags = tcg_gdbstub_supported_sstep_flags;
 
     object_class_property_add_str(oc, "thread",
                                   tcg_get_thread,
diff --git a/gdbstub/gdbstub.c b/gdbstub/gdbstub.c
index 7d8fe475b3..a0755e6505 100644
--- a/gdbstub/gdbstub.c
+++ b/gdbstub/gdbstub.c
@@ -383,27 +383,13 @@ static void init_gdbserver_state(void)
     gdbserver_state.last_packet = g_byte_array_sized_new(MAX_PACKET_LENGTH + 4);
 
     /*
-     * In replay mode all events will come from the log and can't be
-     * suppressed otherwise we would break determinism. However as those
-     * events are tied to the number of executed instructions we won't see
-     * them occurring every time we single step.
-     */
-    if (replay_mode != REPLAY_MODE_NONE) {
-        gdbserver_state.supported_sstep_flags = SSTEP_ENABLE;
-    } else if (kvm_enabled()) {
-        gdbserver_state.supported_sstep_flags = kvm_get_supported_sstep_flags();
-    } else {
-        gdbserver_state.supported_sstep_flags =
-            SSTEP_ENABLE | SSTEP_NOIRQ | SSTEP_NOTIMER;
-    }
-
-    /*
-     * By default use no IRQs and no timers while single stepping so as to
-     * make single stepping like an ICE HW step.
+     * What single-step modes are supported is accelerator dependent.
+     * By default try to use no IRQs and no timers while single
+     * stepping so as to make single stepping like a typical ICE HW step.
      */
+    gdbserver_state.supported_sstep_flags = accel_supported_gdbstub_sstep_flags();
     gdbserver_state.sstep_flags = SSTEP_ENABLE | SSTEP_NOIRQ | SSTEP_NOTIMER;
     gdbserver_state.sstep_flags &= gdbserver_state.supported_sstep_flags;
-
 }
 
 #ifndef CONFIG_USER_ONLY
