Football Insider have reported that United are considering a move for Republic of Ireland international Jeff Hendrick ahead of the 2020/2021 season.
It is believed that the Red Devils are monitoring the midfielder's situation at Turf Moor, as there has been no indication of an extension yet.
Hendrick has been vital part of Sean Dyche's squad in the Premier League this season, having registered three goals and two assists in 22 starts.
There have also been reports in recent months linking the 28-year-old midfielder with Serie A giants AC Milan and Inter Milan.
Hendrick joins a long list of midfielders who have been linked with the Red Devils ahead of next season, including Jack Grealish, James Maddison, Wilfried Ndidi and Saul Niguez.
However, new reports in England suggest that club-record signing Paul Pogba could sign a new long-term deal, which could end any chance of the club buying another midfielder.