Lees has been sidelined with a grade one hamstring problem since the 2-1 loss at Preston on August 24 and will be assessed in the two training days ahead of this weekend’s trip to the north-east before deciding on whether he may feature.
Speaking after the 2-0 Carabao Cup exit to Everton at Hillsborough, Monk, who confirmed that the groin injury that kept fellow defender David Bates out was only a minor issue, said: “If I am honest, it is a day to day thing and a little bit on how he feels.
“We have still got training days before the weekend and he could come in training and not feel the pain and could be ready to go or he can feel tightness.
“It is a daily thing. But he is progressing and doing really well.”
Monk professed to being pleased with many aspects of his side’s performance against Everton - on a night when he made eight changes, with one eye on the club’s forthcoming busy schedule.
He added: “Overall, a lot of good things happened in the game.
“It was not just about making changes and there were a few other situations I had to consider.
“Obviously, Julian (Borner) and Sam Hutchinson were on four bookings and do I risk that or do it not with three league games coming up in seven days? There’s also that side of it.
“There were a few other (issues) with so many games we have had a short period, can they cope with that with the games coming up as well. It was not just about making changes.
“Of course, the other side of it is that they have all trained exceptionally well since I have come here. They have all been competitive.
“The truth is on the pitch. A few of them deserved their opportunity to play and you need to see it.
“At the end of the day, we are going to need the whole squad for the season, it is not just about the last few games.”