Rashford picked up a knock during his side's FA Cup quarter-final win against Fulham on Sunday.
Pope, who has 10 caps, suffered an injury in Newcastle's 2-1 win at Nottingham Forest on Friday.
Mount is also recovering from an injury and will stay with Chelsea.
Tottenham's Fraser Forster, 35, has been called up to replace Pope but no other replacements are planned by manager Gareth Southgate.
Pope, who has 10 caps, suffered an injury in Newcastle's 2-1 win at Nottingham Forest on Friday.
Mount is also recovering from an injury and will stay with Chelsea.
Tottenham's Fraser Forster, 35, has been called up to replace Pope but no other replacements are planned by manager Gareth Southgate.