diff --git a/hw/i386/x86.c b/hw/i386/x86.c
index ffbda48917fd..0a6c59c724f1 100644
--- a/hw/i386/x86.c
+++ b/hw/i386/x86.c
@@ -313,7 +313,10 @@ void x86_cpu_pre_plug(HotplugHandler *hotplug_dev,
 
     init_topo_info(&topo_info, x86ms);
 
-    env->nr_dies = ms->smp.dies;
+    if (ms->smp.dies > 1) {
+        env->nr_dies = ms->smp.dies;
+        set_bit(CPU_TOPO_LEVEL_DIE, env->avail_cpu_topo);
+    }
 
     /*
      * If APIC ID is not set,
diff --git a/include/hw/i386/topology.h b/include/hw/i386/topology.h
index d4eeb7ab8290..befeb92b0b19 100644
--- a/include/hw/i386/topology.h
+++ b/include/hw/i386/topology.h
@@ -60,6 +60,21 @@ typedef struct X86CPUTopoInfo {
     unsigned threads_per_core;
 } X86CPUTopoInfo;
 
+/*
+ * CPUTopoLevel is the general i386 topology hierarchical representation,
+ * ordered by increasing hierarchical relationship.
+ * Its enumeration value is not bound to the type value of Intel (CPUID[0x1F])
+ * or AMD (CPUID[0x80000026]).
+ */
+enum CPUTopoLevel {
+    CPU_TOPO_LEVEL_INVALID,
+    CPU_TOPO_LEVEL_SMT,
+    CPU_TOPO_LEVEL_CORE,
+    CPU_TOPO_LEVEL_DIE,
+    CPU_TOPO_LEVEL_PACKAGE,
+    CPU_TOPO_LEVEL_MAX,
+};
+
 /* Return the bit width needed for 'count' IDs */
 static unsigned apicid_bitwidth_for_count(unsigned count)
 {
@@ -168,4 +183,12 @@ static inline apic_id_t x86_apicid_from_cpu_idx(X86CPUTopoInfo *topo_info,
     return x86_apicid_from_topo_ids(topo_info, &topo_ids);
 }
 
+/*
+ * Check whether there's extended topology level (die)?
+ */
+static inline bool x86_has_extended_topo(unsigned long *topo_bitmap)
+{
+    return test_bit(CPU_TOPO_LEVEL_DIE, topo_bitmap);
+}
+
 #endif /* HW_I386_TOPOLOGY_H */
diff --git a/target/i386/cpu.c b/target/i386/cpu.c
index 0ad400cd709a..6b159298fea5 100644
--- a/target/i386/cpu.c
+++ b/target/i386/cpu.c
@@ -6290,7 +6290,7 @@ void cpu_x86_cpuid(CPUX86State *env, uint32_t index, uint32_t count,
         break;
     case 0x1F:
         /* V2 Extended Topology Enumeration Leaf */
-        if (topo_info.dies_per_pkg < 2) {
+        if (!x86_has_extended_topo(env->avail_cpu_topo)) {
             *eax = *ebx = *ecx = *edx = 0;
             break;
         }
@@ -7122,7 +7122,7 @@ void x86_cpu_expand_features(X86CPU *cpu, Error **errp)
          * cpu->vendor_cpuid_only has been unset for compatibility with older
          * machine types.
          */
-        if ((env->nr_dies > 1) &&
+        if (x86_has_extended_topo(env->avail_cpu_topo) &&
             (IS_INTEL_CPU(env) || !cpu->vendor_cpuid_only)) {
             x86_cpu_adjust_level(cpu, &env->cpuid_min_level, 0x1F);
         }
@@ -7628,13 +7628,25 @@ static void x86_cpu_post_initfn(Object *obj)
     accel_cpu_instance_init(CPU(obj));
 }
 
+static void x86_cpu_init_default_topo(X86CPU *cpu)
+{
+    CPUX86State *env = &cpu->env;
+
+    env->nr_dies = 1;
+
+    /* SMT, core and package levels are set by default. */
+    set_bit(CPU_TOPO_LEVEL_SMT, env->avail_cpu_topo);
+    set_bit(CPU_TOPO_LEVEL_CORE, env->avail_cpu_topo);
+    set_bit(CPU_TOPO_LEVEL_PACKAGE, env->avail_cpu_topo);
+}
+
 static void x86_cpu_initfn(Object *obj)
 {
     X86CPU *cpu = X86_CPU(obj);
     X86CPUClass *xcc = X86_CPU_GET_CLASS(obj);
     CPUX86State *env = &cpu->env;
 
-    env->nr_dies = 1;
+    x86_cpu_init_default_topo(cpu);
 
     object_property_add(obj, "feature-words", "X86CPUFeatureWordInfo",
                         x86_cpu_get_feature_words,
diff --git a/target/i386/cpu.h b/target/i386/cpu.h
index 6b0573807918..60ebc6378064 100644
--- a/target/i386/cpu.h
+++ b/target/i386/cpu.h
@@ -24,6 +24,7 @@
 #include "cpu-qom.h"
 #include "kvm/hyperv-proto.h"
 #include "exec/cpu-defs.h"
+#include "hw/i386/topology.h"
 #include "qapi/qapi-types-common.h"
 #include "qemu/cpu-float.h"
 #include "qemu/timer.h"
@@ -1892,6 +1893,9 @@ typedef struct CPUArchState {
 
     /* Number of dies within this CPU package. */
     unsigned nr_dies;
+
+    /* Bitmap of available CPU topology levels for this CPU. */
+    DECLARE_BITMAP(avail_cpu_topo, CPU_TOPO_LEVEL_MAX);
 } CPUX86State;
 
 struct kvm_msrs;
diff --git a/target/i386/kvm/kvm.c b/target/i386/kvm/kvm.c
index e68cbe929302..2cf04e9c9186 100644
--- a/target/i386/kvm/kvm.c
+++ b/target/i386/kvm/kvm.c
@@ -50,6 +50,7 @@
 #include "hw/i386/apic_internal.h"
 #include "hw/i386/apic-msidef.h"
 #include "hw/i386/intel_iommu.h"
+#include "hw/i386/topology.h"
 #include "hw/i386/x86-iommu.h"
 #include "hw/i386/e820_memory_layout.h"
 
@@ -1920,7 +1921,7 @@ int kvm_arch_init_vcpu(CPUState *cs)
             break;
         }
         case 0x1f:
-            if (env->nr_dies < 2) {
+            if (!x86_has_extended_topo(env->avail_cpu_topo)) {
                 cpuid_i--;
                 break;
             }
