The one-cap England international has not played for the Red Devils since January 2022, shortly before his arrest on suspicion of rape and assault following allegations posted online.
Greenwood was further arrested on suspicion of sexual assault and making threats to kill while in custody, and he was due to face trial on charges of attempted rape, assault occasioning actual bodily harm and engaging in controlling and coercive behaviour in November 2023.
However, the Crown Prosecution Service subsequently dropped all charges against the 22-year-old due to key witnesses withdrawing and new material coming to light, and Man United were believed to be open to letting him resume his career at Old Trafford.
News of the Red Devils' plans sparked huge uproar, though, leading the club to U-turn on their decision and instead ship Greenwood out on loan to Getafe, where he contributed 10 goals and six assists from 36 matches.
Man United 'offered Christos Mandas' in Greenwood deal
Greenwood's Man United contract still has another 12 months left to run, but despite Sir Jim Ratcliffe leaving the door open for him to don the Red Devils strip again, a permanent sale is thought to be on the cards.
As links with Barcelona and Atletico Madrid have gone cold, Italian trio Lazio, Juventus and Napoli are believed to be in a three-way fight for the Englishman's services, and the former have now opened talks over a deal.
According to Tuttomercatoweb, Lazio president Claudio Lotito has baulked at Man United's €40m (£33.8m) asking price for Greenwood, and he has instead put forward two alternative proposals.
One of those involves Lazio paying €18m (£15.2m) and a 50% sell-on clause, while the other would see Man United pocket the same initial amount while also receiving goalkeeper Christos Mandas in return.
The 22-year-old Greece international played second fiddle to Ivan Provedel in the 2023-24 campaign and made just 12 appearances for Lazio last season, albeit while keeping a respectable six clean sheets.
Mandas only arrived at Lazio from OFI Crete last year and is contracted to the Biancocelesti for another four seasons, but the Serie A side are willing to sanction a departure if it helps them land Greenwood.
Why Man United should be open to Mandas deal
Both Erik ten Hag's side and noisy neighbours Manchester City are thought to have taken a liking to Mandas, as the reigning Premier League champions could lose Saudi Pro League-linked Ederson in the coming weeks.
As well as getting one over their bitter rivals, Man United accepting Lazio's player-plus-cash offer would see Ten Hag solve a goalkeeping conundrum which could become more complicated later on in the summer.
Andre Onana will be number one no matter what happens, and Ten Hag was highly reluctant to give Altay Bayindir opportunities to impress last season; the Turkey international made just one appearance when Onana was at the Africa Cup of Nations.
Bayindir could now be tempted by a move back to Turkey, and with there being no guarantees that Tom Heaton will stay beyond the summer, Mandas's arrival would prevent a goalkeeping crisis from occurring.