Alternatively, to avoid recompiling clang, call ./configure with:
./configure CFLAGS=-Ifull/path/relative/to/asm CXXFLAGS=-Ifull/path/relative/to/asm
for example, in your case that is:
./configure CFLAGS=-I/usr/include/i386-linux-gnu CXXFLAGS=-I/usr/include/i386-linux-gnu
You can also define CFLAGS and CXXFLAGS as environment variables. Two examples:
CFLAGS=-I/usr/include/i386-linux-gnu CXXFLAGS=-I/usr/include/i386-linux-gnu ./configure
export CFLAGS=-I/usr/include/i386-linux-gnu; export CXXFLAGS=-I/usr/include/i386-linux-gnu; ./configure
I think I have it written down somewhere how to get GCC to output its default search paths, but I can't dig it out now. If you can find that, you can probably just pass these paths to clang.