The Good Morning Britain presenter is famously close with Trump after Morgan won Celebrity Apprentice in 2008, subsequently going on to become Trump's boardroom advisor on the series.
A bemused May turned him down.
The Prime Minister is facing a hard day on all fronts, with rebel Remainers and Leavers both plotting to publicly go against her, just days before the start of summer recess. I said well it's too early to say, ' Trump was quoted as saying by the Daily Mail on Sunday. "Not go into negotiation, sue them".
"It essentially means that, for now, Theresa May will not be facing a no-confidence vote", she added.
He said: "If they do a deal like that, we would be dealing with the European Union instead of dealing with the United Kingdom, so it will probably kill the deal".
But eurosceptics believe it keeps Britain too close to the European Union, and Davis, the former Brexit secretary, warned in the Financial Times on Monday it would deny the government the "freedom to run our own economy".
President Trump also criticized the prime minister's Brexit decisions, saying it could end chances of a bilateral trade deal with the U.S. "Well.I can't talk, y'know I've heard very strongly from a lot of people, you just don't talk about that conversation with the Queen, right?"
It will be a hot summer's day for Theresa May Monday as former foreign secretary Boris Johnson will make his resignation speech before a key vote in Parliament on a Brexit negotiations strategy. Trump claimed Johnson would make a "great prime minister".
NCAA announces upcoming Final Four sites
The city wasn't selected as one of the four host cities for the 2023-26 Final Fours, unveiled by the NCAA on Monday afternoon. The 2021 Men's Final Four will mark the 24th time since 1940 that the men's basketball championship has come to Indianapolis .
Mr Trump said his mother, Mary Anne Trump, who died in 2000 at the age of 88, was a "tremendous fan" of the Queen.
US President Donald Trump told Theresa May she should sue the European Union instead of negotiating a Brexit deal, the British prime minister said. That has infuriated fervent Brexit supporters, who see it as a bad deal.
The size of the threat should become clear on Monday when lawmakers vote on amendments to legislation on the government's post-Brexit customs regime, with leading eurosceptics set to vote in favour of amendments that May opposes and back their own proposals to toughen up her exit plan.
"We need to keep our eyes on the prize".
Blue Origin subjects its rocket to high-altitude escape test
If all goes well, the demonstration may well see Blue Origin closer to flying people on brief trips to space. This year has already been packed with rocket launches, and many of those have come from SpaceX.
When asked by Piers Morgan in an interview given on Friday in Britain whether he was going to run, Trump said: "Well I fully intend to".
However, she insisted that she had yet to see a "workable alternative" to the proposals - agreed by the Cabinet at Chequers - that would ensure trade remained as "frictionless" as possible while avoiding the return of a hard border between Northern Ireland and the Republic.
In one of the rowdiest debates in parliament on Brexit so far, pro-EU Conservative lawmaker Anna Soubry said: "The only reason that the government has accepted these amendments is because it is frightened of somewhere in the region of 40 members of parliament, the hard no-deal Brexiteers, who should have been seen off a long time ago".
Russian Federation passes the baton to Qatar for FIFA World Cup 2022
Which was the best goal? The Qatari leader assured that his country would do all it can to make a success of the 2022 World Cup. I invite all of our friends to come as guests. "We hope to overcome all the difficulties", said the emir.