Shaw, 31, has been Man United’s first choice left-back for over a decade, but last season was the first time he was able to feature in all 38 Premier League games.
Fans were clamouring for the club to sign competition over the summer ahead of a season with Champions League football.
It was widely reported that Newcastle’s Lewis Hall was their preferred option, but he stayed and has since signed a new deal at Saint James’ Park.
Now, according to TeamTalk, United are looking to rectify that next summer and are only willing to offer Shaw a short-term deal should he want to remain at the club.
Shaw’s current contract is set to expire at the end of the current season and United would be willing to let him leave.
It’s understood the defence is set to be Man United’s priority for the next summer transfer window after attacking and midfield rebuilds over the past two.