Can you ask the teacher if s/he notices another child in the class who might make a good friend for your child? Then ask that child over for a play date. Many teachers recommend one on one play dates for kids struggling to make friends at school (at that age). That way a parent can help the kids find common interests, whether it be movies, running around, legos, science experiements, etc.

Sure, it might not be a life-long friendship, but it is also worth trying.