Donald Trump has said Britain would be better off leaving the European Union.
Voters will take part in an in/out referendum on June 23.
The Republican presidential candidate told Fox News: "I think the migration has been a horrible thing for Europe. A lot of that was pushed by the EU.
"I would say that they're better off without it personally, but I'm not making that as a recommendation - just my feeling."
Last month, President Barack Obama faced criticism for wading into the debate, saying he thought Britain should remain in the EU.
Shadow home secretary Andy Burnham is considering running for the mayor of Greater Manchester.
His spokesman said he has not yet made a final decision on whether to stand or not, and that he intends to remain in the shadow cabinet even if he does seek the role.
A spokesman for Mr Burnham said: "Approaches have been made to Andy Burnham to give consideration to this role.
"It is early days and no decision has been taken. Whatever the decision, he will continue to serve the leader of the party and stay in the shadow cabinet."