The footage shows a never-ending line of Trump campaign signs stretching into the future, which he previously shared in June.
It is a “manipulated” version of a Time animation, the magazine said, used to illustrate an October article suggesting Trumpism would live on well beyond the 45th president.
Mr Trump took to Twitter to reshare the video after the Senate voted to acquit him on two charges of abuse of power and obstruction of justice.
It is far from the first time Mr Trump has brought up serving more than two terms in the White House, which is expressly forbidden by the US Constitution.
While he claims to be joking only for the purpose of winding up liberals, some commentators have suggested his repeated references to staying in office could be an attempt to normalise the idea before making a serious attempt.