The Brazilian playmaker is currently on loan at Bayern Munich but is not expected to be kept on on a permanent basis by the Bavarian giants, having struggled to hold down a regular starting role at the Allianz Arena.
Coutinho is also deemed surplus to requirements at his parent club Barcelona, and recent reports suggest that a return to the Premier League is his most likely destination.
Chelsea were thought to hold the keenest interest, while Tottenham Hotspur and Leicester City have also been linked, but Spanish outlet Sport claims that United have now moved to the front of the queue.
The Red Devils are understood to have earmarked Coutinho as a possible replacement for Paul Pogba, who continues to be linked with a move away, and believe that the 27-year-old would be able to play alongside January arrival Bruno Fernandes.
Coutinho still has three years remaining on his contract at Camp Nou but could be available for a cut-price fee after Barcelona were forced to impose a salary cut on players during the coronavirus crisis.
The Brazil international has made 32 appearances for Bayern this season, but only 15 of those have been Bundesliga starts. body check tags ::