Garnacho, 18, is out of contract in 2024 but the source said there is a financial consensus for him to extend his stay at Old Trafford until 2028.
All that remains to be finalised before the terms can be made official are some aspects relating to the Garnacho's image rights.
The new deal will see his salary adjusted according to his new status in Erik ten Hag's squad due to the progress he has made since making his first team debut last April.
Garnacho has since made 27 appearances for United, scoring three goals, and has been one of the revelations of the Premier League season so far.
Negotiations over new terms started a few months ago and a source close to the talks confirmed to ESPN the club and the player have now reached an agreement over the financial elements of the deal and the length of the contract.
His salary will progressively increase as his role in the team grows.
The source says both parties are keen for everything to be tied up and an official announcement could follow in the coming weeks.
Negotiations remain ongoing for United to be sold -- with bids from Qatari banker Sheikh Jassim Bin Hamad Al Thani and British billionaire Sir Jim Ratcliffe confirmed -- and club officials have been told that, for now, it's business as usual meaning contract talks with players are unaffected.
Garnacho, who joined United from Atletico Madrid in 2020, has a Spanish father and an Argentine mother and is eligible to play for both countries.
He has been capped by both Spain and Argentina at youth level and was part of the latter's preliminary squad for the World Cup, although he did not make the final cut in the end and is yet to debut for Lionel Scaloni's world champions.
ESPN'S Rob Dawson contributed to this report.