diff --git a/migration/savevm.c b/migration/savevm.c
index ef707b8c43..1c49776a91 100644
--- a/migration/savevm.c
+++ b/migration/savevm.c
@@ -2455,6 +2455,10 @@ int save_snapshot(const char *name, Error **errp)
     struct tm tm;
     AioContext *aio_context;
 
+    if (migration_is_blocked(errp)) {
+        return false;
+    }
+
     if (!replay_can_snapshot()) {
         error_setg(errp, "Record/replay does not allow making snapshot "
                    "right now. Try once more later.");
diff --git a/target/i386/kvm.c b/target/i386/kvm.c
index 2724800686..b2401d13ea 100644
--- a/target/i386/kvm.c
+++ b/target/i386/kvm.c
@@ -1266,7 +1266,6 @@ int kvm_arch_init_vcpu(CPUState *cs)
     if (!env->user_tsc_khz) {
         if ((env->features[FEAT_8000_0007_EDX] & CPUID_APM_INVTSC) &&
             invtsc_mig_blocker == NULL) {
-            /* for migration */
             error_setg(&invtsc_mig_blocker,
                        "State blocked by non-migratable CPU device"
                        " (invtsc flag)");
@@ -1276,8 +1275,6 @@ int kvm_arch_init_vcpu(CPUState *cs)
                 error_free(invtsc_mig_blocker);
                 return r;
             }
-            /* for savevm */
-            vmstate_x86_cpu.unmigratable = 1;
         }
     }