Scotland goalkeeper Gordon enjoyed a fine season last term, but a number of injuries blighted his campaign.
Gordon has undergone an operation to have a plate removed from his arm as a result of the arm fracture he picked up against Tottenham in November and he has also received hernia treatment.
Black Cats club physician Dr Glen Rae insists the treatment has been successful and that Gordon is well on the road to recovery.
"Craig had the operation to remove the metalwork from his arm (this summer) and has also undergone bilateral hernia repairs. He is now in the final stages of his rehabilitation," Rae told the club's official website.
Republic of Ireland international Reid missed most of the second half of last season with a long-standing calf problem and he was forced to go under the knife in March.
Reid has been given the green light to take part in pre-season training this week after working hard on his fitness over the summer.
"Andy has spent most of the summer working with our staff and he has done well. He will be ready for the start of pre-season training on Wednesday," added Rae.
Rae also revealed Reid's fellow midfielder David Meyler is "progressing very well" after tearing his cruciate ligaments against Manchester United in May.