Italian outlet Tuttosport (h/t Il Bianco Nero, via Luke Gardener of the Daily Star) reported manager Jose Mourinho has sent chief scout Javier Ribalta to watch the Germany international as he considers replacements for Michael Carrick, who is out of contract at the end of the season. Can will be allowed to depart Anfield on a free transfer next summer if his deal expires.
Per Tuttosport, United's Ander Herrera is also yet to pen a new contract, potentially forcing Mourinho to shuffle his midfield. Can is eligible to negotiate with foreign sides in January, with Juventus previously eyeing the player's talents.
Liverpool hope to retain Can, and United's interest could prompt them to move fast in order to slam shut the exit door.
Can recently said he is happy on Merseyside and will not allow economics to decide where he plays his football.
Per Gardener, Can spoke about his decision to stall on a new deal:
"I read it was about money but it isn’t about money.
"It is never about the money. We’ve had a few good meetings and everything is fine. I am happy at Liverpool.
"You never know what will happen in football but I am happy here and I am still contracted here. Everything is fine."
The 23-year-old is a versatile talent who can feature in the centre of the park or in defence. Carrick has been United's prominent defensive midfielder for over a decade, and Mourinho will need a player like Can if he does not convince Herrera to stay.
Herrera had a successful campaign last term as the club won two major trophies, but the Spaniard has started the current season on the bench after the capture of Nemanja Matic from Chelsea.
Can started 26 games for the Reds in the Premier League last term, according to WhoScored.com, and has become a productive member of coach Jurgen Klopp's squad.
In other Red Devils news, United are following the exploits of Phil Neville's son Harvey, who has been called "the new David Beckham" after his performances for Valencia's academy in Spain.
Per Super Deporte (h/t The Sun's Anthony Chapman), the 14-year-old has emerged as one of the brightest talents behind the scenes for Los Che, with his right foot drawing comparisons to Beckham's most deadly weapon.
The winger has previously featured for United and Manchester City, but the Old Trafford giants want to tempt him to join their ranks at Carrington. Tottenham Hotspur are also considering a move for the attacker.
According to Chapman, Beckham has expressed his interest in the teenager's skills, commenting on Phil Neville's Instagram page about his ability.
Beckham said: "Great cross Philip, you been showing Harvey videos of me??," with Neville replying: "Yes mate, morning noon and night haha."
While Harvey Neville would be one for the future, Can could be an important member of the squad immediately. Liverpool cannot afford to lose Can to a bitter rival, but United's recent trajectory could see them become an attractive option for the German.
The signing of Paul Pogba has shaped the direction of Mourinho's midfield, but the Special One is acutely aware of the defensive options he needs at his disposal.
Matic is certainly the first choice to play ahead of the centre-backs on the field, but the United boss will require an additional head once Carrick finally departs the Theatre of Dreams in the summer, as he is expected to.