The Blues and Serie A giants Napoli have shown interest in signing the Argentina international this month with United prepared to listen to realistic offers for the 20-year-old.
But with the mid-season window set to close on 3 February, the clock is ticking.
Garnacho’s preferred destination is thought to be Stamford Bridge with the winger keen to stay in the Premier League if he does leave Old Trafford.
Napoli have not given up hope of striking a deal as they seek a replacement for Khvicha Kvaratskhelia, who completed his move to Paris Saint-Germain this month.
But L’Equipe report Chelsea are now ready to step up their interest and approach United imminently after extensive talks within the club in recent days.
At this late stage in the window, the report claims United’s asking price for Garnacho currently stands at around £80million.
Financial constraints have forced United to consider offers for players previously regarded as untouchable at Old Trafford.
The club are also close to signing Patrick Dorgu from Lecce with an initial £25m deal on the brink of being completed.
United are also interested in signing Mathys Tel from Bayern Munich to boost their meagre options up top but face competition from Arsenal, Chelsea, Tottenham and Aston Villa.
Garnacho meanwhile has not been a natural fit for Ruben Amorim’s new system at the club but the youngster has started his side’s last two games – victories over Rangers and Fulham.
United still have some work to do in the Europa League against Steaua Bucharest on Thursday night but speaking ahead of that game, the Portuguese head coach underlined his desire to keep Garnacho in his squad.
‘I’m happy to have Garnacho here,’ Amorim told TNT Sports. ‘He’s improving a lot. He’s a young talented guy.
‘You want to work with these guys with talent. That’s what drives the coaches to improve the team; to have these kind of players that you know they are going to improve a lot.
‘In football, especially when we are in these situations, sometimes it’s hard, but I don’t want to focus on that. I’m really happy to have Garnacho playing tomorrow [Thursday].’