The multimillionaire Apprentice boss and former Labour peer was appointed “Enterprise Champion” by Gordon Brown in 2009.
But when asked about Mrs May in an interview with the Sun, Sir Alan said: “I’d vote for her.”
The business mogul also supported the Prime Minister’s decision not to participate in televised leaders’ debates throughout the election campaign.
He said: “Mrs May is 100 per cent right not to get sucked into a head-to-head slanging match on TV.
“I recall advising Gordon Brown not to do it.
“The only ones who benefit are the TV companies – not the public.”
A longtime Labour supporter, Sir Alan left the party in 2015 for what he called its “negative” stance on business.
And last year he castigated Jeremy Corbyn over his leadership and team, branding them “lunatics”.
He said: “Militants, trots, anti-Semites and terrorist sympathisers all seem to have been welcomed into Labour with open arms.”
Sir Alan’s endorsement came as Corbyn’s election bid received the backing from Hollywood legend Danny DeVito.
The American actor tweeted: “UK. You’ve got the guy. Vote for Jeremy Corbyn… show us how it’s done! #grime4corbyn.”