Assistant coach Gary Neville will delay his arrival after his Valencia side lost a third La Liga game in a row.
Hart and Sterling could be out for four weeks, making them serious doubts for City's Champions League quarter-final.
Winger Sterling has a groin injury, while keeper Hart has a calf problem.
Sterling, 21, limped off during City's 1-0 loss to United, while Hart, 28, was hurt after clearing a poor backpass from Martin Demichelis and went off on a stretcher.
City boss Manuel Pellegrini, asked whether they would miss England's games in Germany on Saturday and against the Netherlands at Wembley on 29 March, said: "I don't think muscle injuries are one week. Normally this is three or four weeks."
Neville, meanwhile, is to stay in Valencia to work with his players after fans called for the ex-England defender to leave following a 2-0 home defeat by Celta Vigo.
The 41-year-old, who said he will link up with the England squad on Thursday, said: "You'll report it as panic, but it is not panic, it is something that's important.
"I have just spoken to Roy Hodgson and I am going to stay back in Valencia. The players train Tuesday, Wednesday, Thursday this week. I feel it's the right thing to do.
"Obviously it's not an ideal situation. I'm the assistant coach for the national team of England, with 60 million people, but I understand the two or three million people in Valencia need my attention this week."
Stoke City midfielder Ibrahim Afellay and Sunderland defender Patrick van Aanholt could feature against England at Wembley after being added to the Netherlands squad.
Coach Danny Blind has been hampered by the withdrawal of several players for next week's friendly matches against France and England.
PSV Eindhoven pair Davy Propper and Jurgen Locadia pulled out on Monday, missing out along with Arjen Robben, Daryl Janmaat, Erik Pieters and Ron Vlaar.
Afellay was a surprise omission from the original squad, while Van Aanholt could make his first international appearance in more than two years.
The Netherlands were World Cup semi-finalists in 2014, but have failed to qualify for Euro 2016.

The fire on 1 January destroyed the nursery and infant classrooms at Coed Eva Primary School, Cwmbran.
The teenager, together with six others, was arrested on suspicion of arson with intent to endanger life.
The others, two aged 15, two aged 19, a 16-year-old and a 21-year-old, were released without charge last month.
A reward of up to ??5,000 is being offered by Crimestoppers for information about the fire that leads directly to an arrest and conviction.

Welsh activist John Rees-Evans said Mr Nuttall was effectively powerless without the support of the national executive committee (NEC).
Elections are currently taking place for the ruling body.
Former leader Nigel Farage had a difficult relationship with the NEC.
Mr Rees-Evans came third in the leadership contest with 2,775 votes (18.1%). Mr Nuttall won with 9,622 votes (62.6%), while Suzanne Evans came second with 2,973 votes (19.3%).
"Constitutionally, the role of the leader is limited in terms of determining the direction the party may take," Mr Rees-Evans told BBC Radio Wales' Good Morning Wales programme.
"He needs the support of the NEC and if he doesn't have that support he is effectively powerless."
He hoped that Mr Nuttall would get that support.
"Right now we're in the middle of an NEC election," he said.
"I shall do my very best to try to support candidates that I think will back him and do believe in some of the principles I have stood for very overtly during my campaign.
"I'm hopeful he will get it, but under the present NEC I'm afraid I wouldn't be hopeful."
The NEC was alleged to have "defied" former UKIP Wales leader Nathan Gill over the selection of assembly candidates at the beginning of 2016.
Ex-leader Nigel Farage had publicly criticised one UKIP assembly candidate, Gareth Bennett, as not the sort of person the party would be proud to have as an assembly member.
But despite that the NEC rejected calls to deselect him. Mr Bennett went on to become an AM.
Joe Hart and Raheem Sterling are set to miss England's friendlies with Germany and the Netherlands after being injured during Manchester City's derby defeat by Manchester United on Sunday.
[NEXT_CONCEPT]
A 15-year-old boy who was arrested following an arson attack on a Torfaen school has been released without charge.
[NEXT_CONCEPT]
A defeated UKIP leadership candidate has said he is not "hopeful" that new leader Paul Nuttall will get the support he needs from the party's ruling body.