Downing was expected to join either Liverpool or Tottenham this summer before he suffered a knee injury last week.
Asked if Downing's injury could ironically keep him at the Riverside Stadium, Southgate said: "Possibly, depending on time-scale.
"But if he is here, it probably means he won't be available for the early part of the season anyway, so it is a bit of a double-edged sword.
"I guess we have just got to see how things progress.
"Even after the operation, a player who is highly motivated like Stewart and has a real desire to get back as quickly as possible will always get back quicker than players of a different mentality."