Bywater has missed the last two matches with a back problem, with on-loan Liverpool stopper David Martin deputising.
The Rams' number one is responding well to treatment, though, and Clough is optimistic he could return at Hillsborough.
"Stephen is coming along well and the signs are good. He is absolutely desperate to play but we don't want him to rush himself back and be out for longer," said Clough. "We will see how he responds to a bit of light training."
Steven Davies missed the 2-2 draw against Middlesbrough in midweek with a tight hamstring and the striker remains a doubt.
Winger Gary Teale came through 90 minutes in a behind-closed-doors game this week as he continued his return from a torn calf muscle but this game will come too soon for the Scot, whose last appearance was as a substitute at the start of February.