David Moyes has endured a difficult start to his Old Trafford tenure as United have won just one of their opening three games and have slipped five points behind early pacesetters Liverpool.
Beaten at Anfield on September 1, 24 hours later United suffered a disastrous transfer deadline day when they failed to secure a succession of targets and ended up only bolstering their squad with Moyes' former player at Everton, Marouane Fellaini.
Even that deal brought negative headlines given it ended up costing ?4million more than the ?23.5million clause in the Belgian's contract that Moyes allowed to expire on July 31.
Wilkins does feel Moyes will eventually prove to be an astute appointment as Sir Alex Ferguson's successor.
But in the short term, amid reports of a wide-spread revamp of United's scouting system and executive vice-chairman Ed Woodward getting plenty of flak for failing to land any of the club's major summer targets, Wilkins can see problems.
"David Moyes will do an excellent job, but I fear for Manchester United this season," Wilkins told talkSPORT.
"Fellaini was a very good buy but I think they needed more players, especially on the European front.
"Every side in the Champions League has reinforced, and United have to a degree, but not as well as I'd have liked to see them do."
As Moyes inherited a squad that swept to the Premier League title by an impressive 11 points last term, it would be a major surprise if United were not contending again this year.