diff --git a/Compiler/src/cicache.jl b/Compiler/src/cicache.jl
index 9c528bc0ae822..4d188dbbc3450 100644
--- a/Compiler/src/cicache.jl
+++ b/Compiler/src/cicache.jl
@@ -14,7 +14,7 @@ end
 function setindex!(cache::InternalCodeCache, ci::CodeInstance, mi::MethodInstance)
     @assert ci.owner === cache.owner
     m = mi.def
-    if isa(m, Method) && m.module != Core
+    if isa(m, Method)
         ccall(:jl_push_newly_inferred, Cvoid, (Any,), ci)
     end
     ccall(:jl_mi_cache_insert, Cvoid, (Any, Any), mi, ci)
diff --git a/test/precompile.jl b/test/precompile.jl
index f92a2cc62ef0d..2ee24a71dc62e 100644
--- a/test/precompile.jl
+++ b/test/precompile.jl
@@ -2145,6 +2145,29 @@ precompile_test_harness("No backedge precompile") do load_path
     end
 end
 
+precompile_test_harness("Pre-compile Core methods") do load_path
+    # Core methods should support pre-compilation as external CI's like anything else
+    # https://github.com/JuliaLang/julia/issues/58497
+    write(joinpath(load_path, "CorePrecompilation.jl"),
+          """
+          module CorePrecompilation
+          struct Foo end
+          precompile(Tuple{Type{Vector{Foo}}, UndefInitializer, Tuple{Int}})
+          end
+          """)
+    ji, ofile = Base.compilecache(Base.PkgId("CorePrecompilation"))
+    @eval using CorePrecompilation
+    invokelatest() do
+        let tt = Tuple{Type{Vector{CorePrecompilation.Foo}}, UndefInitializer, Tuple{Int}},
+            match = first(Base._methods_by_ftype(tt, -1, Base.get_world_counter())),
+            mi = Base.specialize_method(match)
+            @test isdefined(mi, :cache)
+            @test mi.cache.max_world === typemax(UInt)
+            @test mi.cache.invoke != C_NULL
+        end
+    end
+end
+
 # Test precompilation of generated functions that return opaque closures
 # (with constprop marker set to false).
 precompile_test_harness("Generated Opaque") do load_path