United have endured a turbulent season under David Moyes, who replaced long-serving manager Sir Alex Ferguson in May.
The Manchester club were knocked out of the UEFA Champions League quarter-finals by defending champions Bayern Munich on Wednesday, ending any hopes of silverware this season.
United also look set to miss out on Champions League football next season for the first time in 19 years, with the club languishing in seven position, seven points adrift of fourth-placed Arsenal.
And Fletcher, who appears to have overcome an inflammatory bowel disease, says it is time for the team's under-performing stars to prove their worth with Moyes expected to ring the changes at season's end.
"It is time to show the manager that you deserve to be at this club," Fletcher said.
"If you get a chance to play, you have to go and impress the manager and show him that you are capable of being here next year.
"Go and put in performances because the manager will be thinking of next season, no doubt about that. You have to make sure that you are one of the names that he still wants."
Moyes is expected to overhaul an aging United squad in the coming months, with captain Nemanja Vidic set for Inter Milan.
Rio Ferdinand, Patrice Evra and Javier Hernandez face uncertain futures, while Bayern midfielder Toni Kroos has been tipped to move to Old Trafford in a big-money deal.
"He will definitely look back on this season and realise it was a disappointment but I fully expect there to be some signings," the Scottish midfielder said.
"People expect signings in the summer, there is no doubt about that, but that is always the case at Manchester United."
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