Mount's existing deal expires next summer and Chelsea would rather cash in now than lose him for nothing in 2024 if no agreement over an extension can be reached.
Sources have told ESPN that Mount is open to moving to Old Trafford and so United are now holding internal discussions over tabling a formal offer.
It is unclear exactly what Chelsea's asking transfer fee is for Mount. One source suggested it is as high as £60 million but interested clubs will believe they can secure a deal for less given the short time remaining on his contract and Chelsea's need to move on players to trim a bloated squad.
Chelsea will hope other clubs formalise their interest to drive the fee up. Liverpool remain keen but have yet to pursue a deal and recently shifted their attention elsewhere as they try to wrap up a move for Brighton's Alexis Mac Allister.
Premier League champions City are in talks with Chelsea to secure a deal for Mateo Kovacic and Mount has so far not been discussed. Reports have linked Arsenal with a move for Mount but their first priority remains trying to sign Declan Rice from West Ham United with Moises Caicedo from Brighton also on their radar.
Mount has not played for Chelsea since April due to surgery on a nagging pelvic injury. His last start came in February's 1-0 home defeat to Southampton under former boss Graham Potter.
The England international is an academy graduate but sources said talks have stalled in recent months in part over his reluctance to accept Chelsea's desire to commit him to a long-term contract, similar to the six-year deal Reece James signed in September.
James's new deal is worth around £250,000-a-week but Mount is not thought to have been offered a comparable salary.