The winger, in the final year of his Goodison Park contract, is understood to be on the list of names drawn up by manager Rafa Benitez.
Benitez is looking to sign a number of players, including a winger, in the window.
And Lennon, 30, is one option for United, who have been involved in protracted talks with Chelsea over a half-season loan for Kenedy.
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Asked about Lennon, Benitez said: "(There have been) a lot of names in the press.
"We can talk about names, maybe. He was the last name, but in a couple of hours there will be another name."
Benitez has been assured by owner Mike Ashley that there will be funds available to sign reinforcements this month.
"We had a meeting," said Benitez, whose side take on Premier League leaders Manchester City at the Etihad Stadium tomorrow.
"Everyone knows what we need and the club will try to sign these players."