Reports in recent days have suggested the central defender is facing an uncertain future, having failed to win back a regular starting place under Jose Mourinho during the final few weeks of the season.
The powerful Ivory Coast international also had to settle for a place on the bench in last weekend's FA Cup final defeat to Chelsea, with Chris Smalling and Phil Jones preferred at the heart of the Red Devils' rearguard.
Bailly was widely recognized to be United's best defensive option after a series of impressive displays following his £30m switch from Villarreal back in 2016.
The 24-year-old, however, has been plagued by a series of niggling injuries during the last 12 months and Carrington insiders claim that has halted a large part of his progression under Mourinho.
The United boss remains a fan of the player and despite him looking to recruit £50m-rated Toby Alderweireld from Tottenham, Bailly is still seen as a major part of his squad make-up for next season.
Bailly has his admirers in Spain but his name is not believed to be on the list of clear-outs planned by the United hierarchy this summer.