Rafael da Silva could miss the Manchester derby on September 22 due to the hamstring injury he sustained in Manchester United’s Community Shield win over Wigan.
And United manager David Moyes also expects to be without striker Javier Hernandez, and wingers Ashley Young and Nani for the game against Chelsea on Monday.
Hernandez has a leg problem, Nani has a groin injury and Young has struggled with his ankle in recent weeks.
And Moyes said: “We've lost Rafael for three to four weeks. The likes of Young, Nani and Chicharito [Hernandez] are still recovering -- hopefully they're not too far away. It's just a case of getting them back up to speed.
"So we've got two or three coming back from really the effects of not having a proper pre-season because they came back from international duty a bit late. Hopefully they're all not too far away now."
Moyes has pinpointed the Chelsea game as a crucial fixture if United are to retain their Premier League title.
The former Everton manager said: “I came for this sort of level of game but I also came to win trophies. To do that you have to beat the likes of Chelsea.
“It's a great first home game for us to have. They have started strongly, have good players and are a good team. There's not a big change to the team -- they just have a new manager, a bit like us.”
Monday’s game pits Moyes against Blues boss Jose Mourinho, whom he faced during the Portuguese’s first spell at Stamford Bridge.
“I really like Jose. He's had great success,” Moyes said. “I've not seen him for a long time so I’m looking forward to seeing him.”