diff --git a/@xen-orchestra/web-core/lib/components/select/VtsSelect.vue b/@xen-orchestra/web-core/lib/components/select/VtsSelect.vue
index 73a7459ff5..0ce4314e7a 100644
--- a/@xen-orchestra/web-core/lib/components/select/VtsSelect.vue
+++ b/@xen-orchestra/web-core/lib/components/select/VtsSelect.vue
@@ -24,6 +24,7 @@
               :placeholder="searchPlaceholder"
               right-icon="fa:magnifying-glass"
               accent="brand"
+              detached
             />
           </div>
         </template>
diff --git a/@xen-orchestra/web-core/lib/components/ui/input/UiInput.vue b/@xen-orchestra/web-core/lib/components/ui/input/UiInput.vue
index 69397d06a3..68c15d3e58 100644
--- a/@xen-orchestra/web-core/lib/components/ui/input/UiInput.vue
+++ b/@xen-orchestra/web-core/lib/components/ui/input/UiInput.vue
@@ -52,12 +52,14 @@ const {
   required,
   disabled,
   id,
+  detached,
 } = defineProps<{
   accent: InputAccent
   id?: string
   required?: boolean
   disabled?: boolean
   readonly?: boolean
+  detached?: boolean
   type?: InputType
   icon?: IconName
   rightIcon?: IconName
@@ -82,7 +84,7 @@ const attrs = useAttrs()
 
 const inputRef = ref<HTMLInputElement>()
 
-const wrapperController = inject(IK_INPUT_WRAPPER_CONTROLLER, undefined)
+const wrapperController = detached ? undefined : inject(IK_INPUT_WRAPPER_CONTROLLER, undefined)
 
 const accent = useMapper<LabelAccent, InputAccent>(
   () => wrapperController?.labelAccent,
diff --git a/CHANGELOG.unreleased.md b/CHANGELOG.unreleased.md
index bec8061ffa..3c6f380110 100644
--- a/CHANGELOG.unreleased.md
+++ b/CHANGELOG.unreleased.md
@@ -38,6 +38,7 @@
 - [XO-Server] Log a xo-server waiting for a soft stop in background (PR [#9994](https://github.com/vatesfr/xen-orchestra/pull/9994))
 - [Backup-repository] Properly unmount and cut connection on stop/disconnect/forget (PR [#9994](https://github.com/vatesfr/xen-orchestra/pull/9994))
 - [xo-proxy] Fix invalid parameters error message in listVmBackups (XS update for example) (PR [#10035](https://github.com/vatesfr/xen-orchestra/pull/10035))
+- [Web-core] Fix the required asterisk disappeared as soon as the dropdown was opened (PR [#10032](https://github.com/vatesfr/xen-orchestra/pull/10032))
 
 ### Packages to release