Jefferies confirmed on Wednesday that Driver would miss at least the next two weeks with a torn thigh muscle.
The 22-year-old former England Under-21 international has only recently returned from the tendonitis which has dogged him for virtually the whole campaign.
Jefferies has now admitted Driver's knee remained a concern and the Jambos boss is giving serious consideration to not picking the player for the final five games of the campaign to allow him to regain full fitness over the summer.
He said: "I'm not going to risk it. I want him fresh to fully recover in time, get a break and pre-season training.
"Hopefully, that period will give him time to heal properly, both on his knee and thigh."
Driver will definitely miss Sunday's Scottish Premier League game at Rangers but there is better news on the injury front regarding Michael Stewart, Jason Thomson, Dawid Kucharski and Ismael Bouzid, who could all feature at Ibrox.
Captain Stewart returned to training on Thursday following a calf problem, Thomson has recovered from an ear infection, while Kucharski and Bouzid (both hamstring) are also fit again.
Gary Glen (hamstring) is extremely doubtful, while Jose Goncalves, Ryan Stevenson (both knee), Janos Balogh (wrist), Marian Kello (hand), Gordon Smith (groin) and Johnny Stewart (knee) are all still out.