Mr Foot said he didn't believe that the party's recent decision to create a vetting panel to draw up a shortlist of candidates would rule out the MP for Brent East.
"I don't think it's possible to stop him by decent means and so I don't think he will be stopped and I hope he isn't," Mr Foot said.
Mr Foot, who is the most senior Labour figure to come out in support of the former GLC leader, said that it was clear Mr Livingstone should be given the chance to stand. "I don't think there's any reason why he should be blocked. You can't put a black ball in elections like that.
"The whole thing has to be absolutely clear and the party membership will see that justice is done.
"He loves London, there's no doubt about that, and he can speak for London. And he speaks in an accent that Londoners understand. That's part of the reason, no doubt, that he's so popular in the party."