Both sides go into Sunday's contest in desperate need of points, with the Whites on a six-game losing run while the Canaries have not won a Premier League fixture since January 21 when they beat relegation rivals Watford.
Byram, who made over 100 appearances for Leeds between 2012 and 2016, missed Norwich's defeat to Chelsea on Thursday night due to fatigue.
Christoph Zimmermann and Mathias Normann were both withdrawn at half time against the Blues but are expected to be available for selection at Elland Road.
"Sam (Byram) we are going to have a look at. He is a little bit fatigued," said Smith.
"I am hopeful he will be okay. All the lads that played last night's game, came through it. We should have them available for Sunday."
Norwich were 2-0 down after 14 minutes against Chelsea but a Teemu Pukki penalty on 69 minutes gave them hope of salvaging something before Kai Havertz sealed victory for the visitors on 90 minutes.
Smith wants to see the same performance levels at Elland Road that his side produced in the second half, in what will be a huge game for both sides.
"It is really big for both teams, because we are both on a losing run. We know we have to get points because we have been sat on 17 points for too long," added Smith.
"We can go and play with a bit more freedom, that is what we did last night in the second half. That is the freedom we have to take into Sunday's match."