"She decided no I'm stopping at home, I'm still looking after the baby, I'm still on maternity leave."
Mr Graham added: "That was ok until Wimbledon started and then she went out again."
Meghan, who has previously labelled President Trump divisive is said to not want to move back to the US while he's still in power, according to the Daily Mail.
Ahead of the 2016 election, she also told Comedy Central's The Nightly Show with Larry Wilmore she was considering remaining in Toronto, where she filmed the USA Network's "Suits," if Trump won.
It comes as President Donald Trump said on Sunday that the United States would not pay for security protection for Britain's Prince Harry and his wife, Meghan, who, according to media reports, have settled in Los Angeles.
Trump wrote on Twitter that "now they have left Canada for the US however, the US will not pay for their security protection. They must pay!"
In January, the couple said they would step away from their royal duties.
A spokeswoman for the couple said later in a statement: "The Duke and Duchess of Sussex have no plans to ask the US Government for security resources. Privately funded security arrangements have been made."
The British Embassy in Washington did not immediately respond to a request for comment.
Last month, Canada said it would no longer provide security once the couple were no longer working members of the British Royal Family.
The couple had been living for several months with their son, Archie, on Vancouver Island in Canada.
The duke and duchess will formally step down as senior members of the monarchy from Tuesday and have already forged ahead with plans to create their new public roles.
It is said they want to make a change in the "armed forces arena" and will make the military central to their charitable work.
Reports have claimed issues such as medical care and homelessness for veterans and injured service personnel, both in the UK and the United States, are to be a focus of their new charitable organisation likely to be launched in the coming weeks.
The couple are also expected to announce a new name for their SussexRoyal brand in the next few days after they conceded in February the word royal could not be used following their decision to leave the monarchy.
Meghan Markle, 38, and Prince Harry, 35, have left Canada and moved to Los Angeles, where they are thought to be planning a permanent home after stepping back from their royal duties. The couple are said to have taken a private flight to LA but did not say when. But, talkRADIO host Mike Graham noted the Duchess of Sussex previously said she will never live in the US while Donald Trump is President.
Speaking on talkRADIO, Mr Graham said: "She also said at one point she would never live in America as long as Donald Trump was President which is fantastic news for him because he's been able to get his revenge by putting that tweet out about not paying for it."
Royal expert Charles Ray added: "Again, she said I'm never going back to America to live there while he's President.
"Let's not forget when he came over here she used some very lame excuse not to turn up to his state banquet.
"Look, if you are a working member of the Royal Family, unfortunately, you've got to entertain some people you may not like.