Fierce rivals Liverpool are said to have held discussions with the Colombian, who helped Sevilla secure back-to-back Europa League triumphs last term, including netting a brace in a thrilling 3-2 victory over Dnipro in the final.
United are on the lookout for a new forward after the Radamel Falcao experiment failed and are hoping to add another proven marksman to their ranks to go along with Wayne Rooney and Robin Van Persie - though the Telegraph report indicates that Van Persie's future at Old Trafford remains in doubt.
It also states that United have 'taken soundings' over what it would take to land 28-year-old Bacca, but he may not necessarily be among their top targets.
In terms of competition with Liverpool, they have Champions League football to offer whereas a switch to Anfield will mean another crack at the Europa League, while United's spending power is so vast they could probably offer more when it comes to personal terms.
After signing Roberto Firmino from Hoffenheim, there is the question of whether Liverpool feel the need to add Bacca to their ranks as well as they look to solve their own issues in front of goal ahead of next season.
It seems as though Bacca is keen on a move to the Premier League but three other clubs have been mentioned in the report, including Tottenham Hotspur, Newcastle United and Swansea City.