Trump might have intentionally put the rumor out that Giuliani was campaigning for it - maybe even ASKED him to campaign for it - as a stalking horse. It never seemed to make much sense, he has never seemed particularly foreign policy oriented.
Oh, I agree, the idea of Giuliani would never have occurred to me. But, apparently, he does have some international business experience since leaving the Mayoralty. I hope he’s connected to the Administration in a powerful position if that’s what he wants ... who knows if he really wants anything other than to see Trump in the White House? He’s got a nice life in the city he loves.