The Stamford Bridge side have responded to their Premier League rivals and talks are ongoing.
United’s offer is for an initial loan and the clubs are discussing various parameters around that.
The Spain international left-back is viewed at Old Trafford as a good fit for manager Erik ten Hag’s system and at present he is the top candidate.
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Dialogue over the 25-year-old began after Luke Shaw suffered a muscle injury that is set to keep him out for an extended period, with alternative option Tyrell Malacia also on the sidelines.
That leaves 20-year-old Alvaro Fernandez as United’s only recognised player for that position.
Cucurella has been an unused substitute in Chelsea’s first three matches of the new season. Ben Chilwell is ahead of him in the pecking order.
Diogo Dalot operated at left-back for United’s victory over Nottingham Forest on Saturday.
