Lallana's contract at Anfield expires at the end of this season, and the midfielder is expected to leave the club, with no renewal in sight.
Deeney believes that the England international would "walk into 90%" of the teams in the Premier League, including Manchester United's.
"I was just chatting about this with my mates in our group chat – Lallana walks into 90% of teams," Deeney told The United Stand.
"He could play for Man City but I think they're overpopulated... you would take him at United. He'd be in the squad and 100% he improves the squad.
"Lallana can play anywhere across the front line. Tottenham would take him, Everton... Chelsea, yeah."
FIFA earlier today confirmed that expiring player contracts like Lallana's can be extended until the end of the coronavirus-affected 2019-20 season. body check tags ::