Twenty-two-year-old Greenwood is not believed to have a future at Old Trafford following his loan return from Getafe, where he scored 10 goals and provided six assists in 2023-24.
The Englishman has not played for the club since shortly before his initial arrest in January 2022, although charges of attempted rape, assault occasioning actual bodily harm and engaging in controlling and coercive behaviour were dropped last year.
Ligue 1 outfit Marseille and Italian giants Lazio are considered the two frontrunners to sign Greenwood, and the pair are believed to have submitted bids to Man United, who value him at £40m.
According to a report from Italian outlet Calciomercato, Man United have now rejected Lazio's first verbal offer for Greenwood, but there is still optimism on the Biancocelesti's side that a deal can be wrapped up before July 8.
Lazio 'prioritising' Greenwood over Nuno Tavares
However, as Lazio are currently going all out to bring Greenwood to the club, their pursuit of unwanted Arsenal left-back Nuno Tavares has been put on the back burner, to Mikel Arteta's frustration.
The Gunners are determined to shift the Portuguese following his recent loan spell with Nottingham Forest, and a separate report from Calciomercato claims that information is being 'gathered' on Tavares.
The outlet adds that talks are expected to be held with intermediaries in the 'coming days', but that is likely to be after a decision has been made in their Greenwood pursuit and so may be a little while longer.
Lazio's endeavours to sign Greenwood are further complicated by the fact that they are just one of six clubs rumoured to be interested; Atletico Madrid, Napoli, Juventus and Borussia Dortmund have also been linked.
Furthermore, the attacker's preference is said to be a move to France with Marseille, as a desired return to Getafe is unlikely to materialise due to Man United's valuation.
Why do Arsenal want to sell Tavares?
An unknown quantity when he first signed for the Gunners from Benfica in 2021, Tavares played backup to Kieran Tierney upon his arrival, but the Scotsman's injury woes meant that he was always likely to be given an early chance to impress.
The left-back did exactly that with an explosive performance against Aston Villa in October 2021 - his first Premier League start - and he briefly nailed down a place in the team before a disastrous FA Cup outing at Nottingham Forest saw him taken off in the first half.
Tavares did still end his season on a high note with a goal against Manchester United, but his relationship with Arteta was never the same, and there were allegations of poor behaviour during his time at Marseille too.
From a playing sense, the 24-year-old is undoubtedly more suited to a wing-back or potentially winger's role rather than an out-and-out left-back slot, as his defending always leaves a lot to be desired.
Furthermore, as someone who thrives on the overlap while Arteta likes his left-backs to invert, there is simply no place for Tavares in the Emirates ranks anymore.