The 60-year-old actor-turned-presenter hosts Peacock's ultimate game of betrayal and deceit, where members of a group are chosen as Traitors and the rest become Faithful, and it is the job of the Faithful to try to work out who the Traitors are without being "murdered" by their opponents.
Whilst figuring out who are Faithful and who are Traitors, the cast complete tasks to add money to the big prize pot - with the most recent season of The Traitors US split a pot of $US205,000 ($A307,600) four ways.
Alan joked the show would "probably" pay the 79-year-old Republican Commander-in-Chief more than his current salary of $US400,000 ($A600,750) per year.
After The Traitors US claimed the Best Reality Competition Program gong at the 77th Primetime Emmys at the Peacock Theatre in Downtown Los Angeles, California, on Sunday, Alan quipped to reporters in the event's press room: "I'm sure our president would be very good on the show.
"I'm sure he'd have a little chaos and turmoil and treachery, so maybe he'd like to come on and be paid for that, probably better than he gets as president."
The second series of The Traitors US featured John Bercow - the 62-year-old former Speaker of the House of Commons in the UK's Houses of Parliament.
Even though the politician have taken part in the game show, Alan - who began hosting The Traitors US when it debuted in 2023 - previously admitted he despises the idea of President Trump or anyone from his world taking part in his series.
In January, Alan told Vanity Fair: "It's not appetising to me. I think that is too soon - far too soon.
"Also, there's people you think, 'You're still too toxic … You're a toxic influence.'
"There are baddies, like Tom (Sandoval, TV personality-and-musician who was a Faithful in the third season of The Traitors US) came with his baggage, but it's on a different level of toxicity."
Elsewhere in his Vanity Fair interview, Alan said an all-stars version of The Traitors US, where past contestants return to Ardross Castle, Scottish Highlands - where the show is filmed - is a "good idea".
He added: "You don't necessarily have to be a winner. We'd get (drag queen) Peppermint (who was banished as a Faithful first in season two) back.
"I also liked how we'll bring people back for a wee guest appearance, like when (Below Deck star) Kate (Chastain, who was a Faithful in The Traitors US season one) came back in.
"All-stars would be great. I also thought we could do a Drag Race crossover and have Traitors with all drag queens.
"Wouldn't that be funny? Me and RuPaul could duke it out."
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