The Sun says United have reportedly already held transfer talks with Bailey.
The Red Devils are said to have made contact with the 23-year-old's representatives in January, according to journalist Jonathan Shrager.
The report states Tottenham and AC Milan were two other clubs who also sounded out the Jamaican star's availability at the start of the year.
But the Bundesliga ace is believed to be solely focused on performing for Leverkusen for now.
The player's deal at Leverkusen runs until 2023 and the German club are keen to extend his stay but they face a tough ask to get him to re-sign.