Cullen took a whack towards the end of Tuesday's Checkatrade Trophy victory at Cheltenham Town but McCall says the issue has settled down for the West Ham United loanee ahead of the visit of the Lions.
Following recent FA Cup and play-off encounters between the two sides, Saturday's match will be the eighth game in just over two years between City and Millwall.
Billy Clarke is up for selection for the Millwall match after making a successful return from injury as second half sub at Cheltenham, while Filipe Morais has returned to full training following a recent calf problem.
McCall said: "There is no surprise really with Josh - we knew he would put himself up to play.
"He actually wanted to train today (Thursday) because he'd only played for 45 minutes on Tuesday but we put him in the pool with the rest of the lads to help with recovery.
"He is a typical midfielder - he grits his teeth and gets on with it.
"Billy (Clarke) is another available for selection as well.
"He was playing well before his injury so he certainly comes into our thoughts for Saturday.
"Both Billy and Fil (Morais) have looked really sharp in training.
"It might be too soon to throw Fil back in but having him and Billy in training once again has certainly given everyone a lift.
"We have a fully fit squad squad to select from.
"We have Alex Jones and Alex Gilliead back after being cup-tied in midweek and the likes of Darbs (Stephen Darby), Rory (McArdle), Killa (Matthew Kilgallon) and Danny (Devine) coming into the game on the back of strong performances (at Cheltenham)."