diff --git a/src/main/java/com/fasterxml/jackson/databind/introspect/POJOPropertyBuilder.java b/src/main/java/com/fasterxml/jackson/databind/introspect/POJOPropertyBuilder.java
index 550b4a9862..4c9ef45e3d 100644
--- a/src/main/java/com/fasterxml/jackson/databind/introspect/POJOPropertyBuilder.java
+++ b/src/main/java/com/fasterxml/jackson/databind/introspect/POJOPropertyBuilder.java
@@ -394,7 +394,11 @@ public Class<?> getRawPrimaryType() {
 
     @Override
     public boolean couldDeserialize() {
-        return (_ctorParameters != null) || (_setters != null) || (_fields != null);
+        return (_ctorParameters != null)
+            || (_setters != null)
+            || ((_fields != null)
+                // [databind#736] Since 2.16 : Fix `REQUIRE_SETTERS_FOR_GETTERS` taking no effect
+                && (_anyVisible(_fields)));
     }
 
     @Override
diff --git a/src/test/java/com/fasterxml/jackson/failing/RequireSetterForGetter736Test.java b/src/test/java/com/fasterxml/jackson/databind/ser/RequireSetterForGetter736Test.java
similarity index 96%
rename from src/test/java/com/fasterxml/jackson/failing/RequireSetterForGetter736Test.java
rename to src/test/java/com/fasterxml/jackson/databind/ser/RequireSetterForGetter736Test.java
index 222e7f7a03..93409bac5e 100644
--- a/src/test/java/com/fasterxml/jackson/failing/RequireSetterForGetter736Test.java
+++ b/src/test/java/com/fasterxml/jackson/databind/ser/RequireSetterForGetter736Test.java
@@ -1,4 +1,4 @@
-package com.fasterxml.jackson.failing;
+package com.fasterxml.jackson.databind.ser;
 
 import com.fasterxml.jackson.annotation.JsonAutoDetect.Visibility;
 import com.fasterxml.jackson.annotation.PropertyAccessor;