The Blues have also enquired about Borussia Dortmund winger Jamie Gittens, reports claim.
talkSPORT understands United do not intend to sell Garnacho or Kobbie Mainoo, who has also been linked with Chelsea, amid reports they need to cash-in on their homegrown talents.
Until the win over Southampton on Thursday night, Garnacho had not started a league game since the Nottingham Forest clash on 7 December.
United manager Ruben Amorim recently admitted he wants improvements from the youngster.
He responded: "That is clear, he has talent. He needs to learn to play a little bit in a different position. He needs to play better inside.
READ MORE ABOUT CHELSEA
I spent eight hours doing Spurs medical then joined rivals - one director threatened me
Terry was blasted for Villas-Boas revolt that saw Chelsea legends refuse to board plane
"He improved a lot in the recovering position, when he doesn't have the ball, but, doing that, sometimes he's not in the right place to make transitions, like he was in the past, because I prefer to defend and then build up with all the team to make the final third."
While Garnacho continues to have a rocky season, English star Gittens is making waves at Dortmund as their next best young talent.
He was part of Manchester City's youth team between 2018 and 2020 then moved to Germany the September of that year.
Gittens mainly featured in Under-19 competitions but did make his Bundesliga debut as a substitute against Wolfsburg in April 2022.
Most read in Football
Haaland £250m contract, Solskjaer back at the wheel, Everton release PSR update
Tony Mowbray to appoint West Brom assistant who spent nine years with arch rivals
Antony offered Man United escape route - on one condition
Gutted Rory McIlroy gives three-minute speech warning close friend to reverse $5m decision
His senior minutes took a leap last season with 14 league starts but this campaign he has really stamped his mark.
The winger has scored against Bayern Munich as well as reigning Champions League winners Real Madrid as part of a breakthrough 2024/25 season.
The Blues remain active in the transfer market despite a busy summer window which saw them sign the likes of Jadon Sancho and Pedro Neto.
Enzo Maresca is aiming to bolster his squad, who are on a five match winless streak.
Within that run Chelsea have only scored four goals, three of them being from open play and all of those being netted by Cole Palmer.
It is clear they need to be less reliant on the English international who has started every Premier League match this season.
Chelsea are also one winger down after Mykhailo Mudryk was suspended from football over a failed drugs test.
Meanwhile, Christopher Nkunku is being linked with a £60m move to Bayern Munich amid a lack of gametime at Stamford Bridge.