He notoriously accused his predecessor of wiretapping him, something Mr Obama denied. Mr Obama has largely kept his silence.
But the 44th president poked fun at the 45th at a private event this week, when he contrasted Mr Trump’s popularity to that of his landmark healthcare legislation.
CNN said that one attendee at the closed-press and off-the-record event, and hosted by the A&E network for a private audience, paraphrased Mr Obama, by saying: “The Affordable Care Act has never been more popular - and it’s more popular than the current president.”
Mr Trump has had historically low approval ratings, with a recent poll showing that after 100 days in office, just 44 per cent of the public approved of his performance.
By contrast, the same surveys revealed that 47 per cent of Americans approved of the Affordable Care Act, better known as ObamaCare.