If Barack Obama intervenes in the debate over the UK's membership of the European Union then the Government should set out who it wants to win the 2016 US presidential election.
Eurosceptic Tory MP Martin Vickers made the call with the US president due to arrive in the UK on Thursday on a visit which is likely to see him drawn into the Brexit row.
The White House has indicated that Mr Obama will set out his support for a vote for the UK to remain in the EU when he holds a joint press conference on Friday with David Cameron.
However, Leave campaigners believe Mr Obama - and all other international leaders - should stay out of the debate ahead of the referendum on June 23.
Mr Vickers told the House of Commons that if the President does get involved then the UK Government should follow suit and intervene in US domestic affairs.
The Tory MP for Cleethorpes asked Commons Leader Chris Grayling: "In view of the anticipated intervention by the American president into the EU referendum, could the Leader arrange for a statement by our Government setting out which is their preferred candidate for the American presidency and who they would actually like to win the election in November?"
Hillary Clinton and Donald Trump are currently seen as the frontrunners to contest the US election but Mr Grayling insisted the UK will work with whoever wins.
He said: "You tempt me but it is my view that this country should and will work with whoever becomes president of the United States.
"They are our closest allies. They are our longest-standing allies.
"They are a beacon of liberty in the world.
"I'm absolutely certain that we will work with them regardless of who is their president and they will work with us regardless of whether we are inside or outside the European Union."
Meanwhile, Henry Smith, the Tory MP for Crawley, echoed a similar sentiment to Mr Vickers when he asked Mr Grayling: "The United States would rightly never cede its sovereignty to a super-national body so can we have a debate on the protocol that international leaders should not involve themselves in commenting on domestic elections?"
The Commons Leader replied: "I suspect that whatever else around this current debate, President Obama will have picked up the different sides of this argument before he arrives and we will all wait with interest to see what he has to say."