The pair picked up knocks in United’s 2-0 win over Portsmouth at Old Trafford on Wednesday night and the club are waiting to find out the full extent of the damage.
Neville, who started at right-back against Pompey, is to undergo an x-ray on a foot problem while O’Shea will have a scan later to assess the ankle injury he suffered.
Sir Alex Ferguson wasn’t happy with the two tackles that caused both injuries and has already ruled the duo out of Saturday evening’s home clash with Tottenham.
Fergie admitted: “We’ve had a bad time at right-back and now they are both looking at being out for weeks.
“They were both bad tackles but the referee didn’t do anything about either of them and that’s disappointing.”