Host Dana Perino asked Kilmeade whether Trump's remarks at his joint press conference with British Prime Minister Theresa May were an attempt to "not get too entangled in Britain's decision-making on how they're going to do it."
The "Fox & Friends" host agreed, adding Obama warned Britain to, "keep in mind, if you think you're getting a trade deal with us when you get out, you go to 'the back of the queue'."
"Isn't that putting your hand on the scale?"
In 2016, Obama described the Brexit vote as potentially damaging to the British economy. He told reporters the U.S. was focused at the time on a massive trade agreement with the EU and would not prioritize a bilateral deal with the U.K.
"It's not going to happen anytime soon because our focus is in negotiating with a big block of the European Union to get a trade agreement done... U.K. is going to be in the back of the queue," he said.
Visiting Scotland in 2016, then-candidate Trump said the British people were "angry over borders" and declared the U.K. would not be the last EU member to vote to leave the political union.
"They're angry over borders, they're angry over people coming into the country and taking over, nobody even knows who they are," Trump charged. "They're angry about many, many things."
The Associated Press contributed to this report.