The 27-year old was one of few Newcastle players to stand out during disappointing campaign, and he has since been linked with the Premier League champions.
David Moyes is believed to be looking to strengthen his midfield following the retirement of Paul Scholes and a switch to United is something which appeals to the Frenchman.
"Yes of course. I've liked this club for a long time, I like what they do," he told Canal+. "The boss has left but they have appointed a very good successor and he did some good things with Everton.
"They are always well played among the big clubs. Yes for sure, it would be an interesting challenge."
Monaco and PSG have also been reported to be chasing Cabaye, but he says he is unaware of any interest from his homeland.
"I have no direct contact with anyone; maybe my agents are currently in the know.
"As for me, I am here listening. I like England as well. I will need to look at the situation but you never know."