The Red Devils submitted a proposal to sign the Spaniard on a season-long loan deal on Tuesday.
While Chelsea are open to letting Cucurella leave Stamford Bridge, they want his wages covered and a £7m loan fee.
The Blues paid £62m for the then-Brighton full-back in 2022.
But United’s offer was just £2m, leading Chelsea to reject the proposal.
Talks are ongoing between the two clubs as they seek to thrash out an agreement before the transfer window closes.
The full-back is keen on moving to Old Trafford, where he feels he can revive his career.
Cucurella suffered a nightmare debut campaign at Stamford Bridge and he’s yet to play a single minute of football this term.
United are desperate for left-back cover after losing Luke Shaw to injury, while Tyrell Malacia is already sidelined.
The Red Devils have made enquiries for the likes of Nicolas Tagliafico and Sergio Reguilon in the event that a deal for Cucurella fails to materialise.
