As far as I know, you can't be the Labour leader if you're not an MP. Andy Burnham would have to step down as mayor and win a by-election. It's been suggested that Harriet Harman, who's stepping down at the next election, could step down early to allow him to win her mega-safe seat. I can see that going down very badly, as would changing the rules to accommodate him. It's worth remembering that he contested the leadership and lost.