Lees and Julian Borner were back in training this week after injury. But whereas Borner has shrugged off a twisted ankle in time to face Blackburn Rovers, Lees needs more time to recover from a more serious hamstring injury.
Borner went over on his ankle in the warm-up to last week's 0-0 draw with Leeds United, pressing midfielder Sam Hutchinson into action in the heart of the defence.
But manager Monk is taking more time with Lees, who has not played since August. Provided Lees comes through Monday's under-23 game at Burnley, he will be considered to face Monk's old club Swansea, a week on Saturday.
“We're still building up his football fitness,” Monk explained. “He's been on the training field all week, which is good. Every day you get stronger and stronger.
“You can do all the preparation you want in terms of rehab but when you come back to the intensity of training, we have to do right by him and make sure he's at a level where when he is available for selection he can do himself justice. He's still in that phase of building football fitness.
“He'll get a game with the under-23s at the start of next week and we'll build him up again that week, then assess him after that during the two-week period going into the Swansea game to decide whether he's available for that or if he needs a bit more.
“Generally I try to work so that anybody who's been out for over two weeks has a period of building football fitness and the possibility of playing two to three under-23 games to make sure they tick all the boxes.”
Midfielder Massimo Luongo also missed last week's derby with a minor knee problem and will be assessed ahead of the trip across the Pennines.
“It was just a niggle,” Monk said of the Australian's injury. “It was probably a little bit sorer than we originally thought but he's nearly there. We'll assess him tomorrow in terms of whether he's available for the weekend. If not it will be next week but he's progressed really well.”
On paper, Blackburn do not pose as stern a threat as title-chasing Leeds did last week, but Monk has warned his players they cannot take Tony Mowbray's men lightly.
“Playing against Tony's team the last couple of years, I don't think I've had an easy game at Ewood Park at all,” he said.
“When you're going through a tough patch, that next game is the opportunity to respond so we're preparing for and expecting a difficult game, a tough game physically and they have good players so it's the same process.
“At big clubs like Sheffield Wednesday, the expectation will always be there. Regardless of the fact the club's been out of the Premier League for nearly 20 years, the expectation will always be there because that's where the club feels it belongs, quite rightly so. We have to take that responsibility but be realistic, there are going to be patches where you're going to lose a couple of games.
“There's no demand in terms of where we are in the league from within. We don;'t need to focus on that or talk about it. It's about the next game and the next game.
“Consistency is all we can hold ourselves accountable for. In the Championship you have to be at your maximum to get anything out of a game.”