diff --git a/Makefile b/Makefile
index 440313b88419..47ce705660fb 100644
--- a/Makefile
+++ b/Makefile
@@ -355,6 +355,7 @@ STRIP	= $(CCACHE) $(CROSS_COMPILE)strip
 OBJCOPY	= $(CCACHE) $(CROSS_COMPILE)objcopy
 OBJDUMP	= $(CCACHE) $(CROSS_COMPILE)objdump
 OBJSIZE		= $(CROSS_COMPILE)size
+READELF		= $(CROSS_COMPILE)readelf
 AWK		= awk
 GENKSYMS	= scripts/genksyms/genksyms
 INSTALLKERNEL  := installkernel
@@ -415,7 +416,7 @@ KERNELVERSION = $(VERSION)$(if $(PATCHLEVEL),.$(PATCHLEVEL)$(if $(SUBLEVEL),.$(S
 
 export VERSION PATCHLEVEL SUBLEVEL KERNELRELEASE KERNELVERSION
 export ARCH SRCARCH CONFIG_SHELL HOSTCC HOSTCFLAGS CROSS_COMPILE AS LD CC
-export CPP AR NM STRIP OBJCOPY OBJDUMP
+export CPP AR NM STRIP OBJCOPY OBJDUMP OBJSIZE READELF KBUILD_HOSTLDFLAGS KBUILD_HOSTLDLIBS
 export MAKE AWK GENKSYMS INSTALLKERNEL PERL PYTHON UTS_MACHINE
 export HOSTCXX HOSTCXXFLAGS LDFLAGS_MODULE CHECK CHECKFLAGS
 
diff --git a/arch/x86/boot/compressed/Makefile b/arch/x86/boot/compressed/Makefile
index 89b163351e64..676ed22aa700 100644
--- a/arch/x86/boot/compressed/Makefile
+++ b/arch/x86/boot/compressed/Makefile
@@ -95,7 +95,7 @@ vmlinux-objs-$(CONFIG_EFI_MIXED) += $(obj)/efi_thunk_$(BITS).o
 quiet_cmd_check_data_rel = DATAREL $@
 define cmd_check_data_rel
 	for obj in $(filter %.o,$^); do \
-		${CROSS_COMPILE}readelf -S $$obj | grep -qF .rel.local && { \
+		$(READELF) -S $$obj | grep -qF .rel.local && { \
 			echo "error: $$obj has data relocations!" >&2; \
 			exit 1; \
 		} || true; \