He also said Boris Johnson would make a "great prime minister".
May has previously said she does not believe her Brexit plans should rule out a trade deal with the United States. It is not considered appropriate to call the Queen by her first name - a gaffe that Nelson Mandela made in 2014 - and it is never okay for people to use her nickname Lilibet, which is reserved exclusively for very close family members.
"And on that matter, for example, I think it's fair to say that maybe some point down the line there might be a UK-US trade agreement, but it's not going to happen any time soon because our focus is in negotiating with a big bloc, the European Union, to get a trade agreement done", Obama said in a joint appearance in London with then-PM David Cameron.
"I think whenever his detractors go after him, it makes him double down and it actually encourages him to keep going and prove everybody wrong", she said. "Deals that take too long are never good ones".
Mr Morgan, the forthright journalist and broadcaster, hit back and questioned why the London mayor had not been so vocal over the visit of controversial Turkish President Recep Erdogan.
President Donald Trump said he felt "unwelcome" in London after its mayor, Sadiq Khan, permitted a 20-foot-tall angry "Trump Baby" blimp depicting him to be flown during his visit to the UK. Two years ago, Khan first crossed Trump's radar by criticizing his call for a ban on Muslim immigration to the US.
Donald Trump, 72, is about to visit the United Kingdom for the first time since being elected president in November 2016, and the British people aren't prepared to give him a warm welcome.More news: Just 38 children guaranteed to be reunified by border separation deadline
Trump also criticised May in a press conference in Brussels following a North Atlantic Treaty Organisation summit there just before flying to London, casting doubt on whether she will deliver on British voters' intentions when they backed leaving the European Union in a 2016 referendum.
President Donald Trump will get the red-carpet treatment on his brief visit to Britain beginning today: military bands at a gala dinner, lunch with the prime minister at her country residence and tea with the queen at Windsor Castle before flying off to one of his golf clubs in Scotland.
But for many British diplomats, Brexit marks the collapse of a 70-year strategy of trying to balance European integration with a USA alliance based on blood, trade and intelligence sharing. Although Trump has said this practice will be stopped, thousands of children remain separated from their parents and face great difficulty locating their relatives. The police officers overseeing Trump's trip to the United Kingdom are being forced to sleep in unacceptable conditions worse than cells. "I think they like me in the UK". I am just saying I think he would be a great Prime Minister.
Mr Trump's mother was originally from the Isle of Lewis, and he has often spoken of his love for Scotland and its people.
As the Trumps dined with the Mays, protests in the British capital took place outside Winfield House, the residence of US Ambassador Woody Johnson.
As well as in London, protests are expected to take place in Bristol, Newcastle, Leeds, Cambridge and Cardiff after Trump arrives here on Thursday.
Mr Trump and his wife Melania flew from London by Marine One helicopter and swept into the palace courtyard in the armoured presidential limousine nicknamed The Beast.
"Theresa May has invited President Trump to our country at a time when his risky and inhumane policies are putting the lives and wellbeing of millions of people at risk", he said.