Spanish newspaper Marca (h/t Metro) reported United coach Jose Mourinho attempted to capture the France international, with the 22-year-old impressing as his country marauded to World Cup success at Russia 2018. The Red Devils were reportedly willing to double Lucas' wages in order to bring him to Old Trafford, but the player opted to remain in the Spanish capital.
The Marseille-born star, who can play at left-back or centre-back, has seen his stock rise in the past 12 months, and United had been linked with defensive players throughout the summer transfer window.
Per Marca, Lucas' release clause was raised to £71 million after signing fresh terms with Atleti, but this did not stop United from meeting the La Liga club's desired fee. The player decided his immediate future remained with his current side, but United and Manchester City are expected to compete for his signature in January.
Lucas started seven matches for France at the 2018 FIFA World Cup, with Les Bleus defeating Croatia in the final, as United midfielder Paul Pogba shined for the newly-crowned world champions.
According to Marca (h/t Jack Rathborn of the Mirror), the defender recently reaffirmed his commitment to his club, saying: "I'm still at the club of my life."
United's defence has been tested in the opening weeks of the new season, with Mourinho unable to find a satisfactory combination in his back four.
Lucas would have been a perfect addition if Mourinho had opted for a 3-5-2 formation, but the reintroduction of Luke Shaw has strengthened the club at left-back.
Shaw was recently injured after featuring for England, but the defender has displayed promising form throughout pre-season after a difficult period at the Theatre of Dreams.
Per Metro, Mourinho was desperate to capture either Harry Maguire and Toby Alderweireld to solidify his options, but United failed to land any of their key defensive targets.
The international break came at the wrong time for Mourinho after his team beat Burnley following defeats to Tottenham Hotspur and Brighton & Hove Albion, and the Special One will be hoping his side can improve their consistency as the UEFA Champions League campaign approaches.
Neither Eric Bailly, Victor Lindelof, Chris Smalling or Phil Jones have convinced in recent months, potentially opening the door for Argentina international Marcos Rojo to return to the starting XI after he recovers fully from injury.