The Rams had been trying to sign a keeper on loan to provide cover for first-choice stopper Stephen Bywater and had an approach for Blackburn's Frank Fielding knocked back by the Premier League club.
Boss Nigel Clough said: "Saul is not as bad as we first thought. At first we thought it would be four to six weeks and if he was an outfield player it probably would be. But he had a scan this week and it has improved tremendously in the last 48 hours or so.
"With him being a keeper we can heavily strap it and it won't restrict his movement too much.
"He will miss this Saturday against Reading but he could be okay for the West Brom game and if we could get him back on the bench it might mean we don't need to get another goalkeeper in, which could free up another possible loan elsewhere if it was needed."