The midfielder was absent due to a knee injury as the Reds` proud 36-game unbeaten league run at the City Ground was ended by Hull on Saturday.
"Paul should be okay for Tuesday. That is a boost because we missed him against Hull," said Davies. "We missed him for his leadership, his positional play and his organisation."
McKenna was one of seven key players sidelined by injury on Saturday, with Guy Moussi, Nathan Tyson, Dexter Blackstock, Robbie Findley, Kelvin Wilson and Joel Lynch also missing out.
Davies added: "We are probably looking at Swansea (on March 19) for a number of the players to come back. We could be looking at Tyson and Moussi for that game."
Dele Adebola, Garath McCleary and David McGoldrick are available for recalls should Davies wish to make further changes at Bramall Lane.