The defender has resumed light training, having missed the last eight fixtures with a hamstring injury.
Although Friday's trip to Cardiff City will come too soon for Lees, Wednesday's club captain may "potentially" be involved when the Championship club entertain Stoke City next Tuesday.
Garry Monk, the Owls boss, said: "He is back out on the field and doing most of the training.
"He should be back in full training on Sunday when we are back in.
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"The game on Friday will probably come a little bit too soon but he could potentially be in the reckoning for Stoke."
Lee has yet to feature under Monk.
In his absence, Dominic Iorfa has formed a strong partnership with fans' favourite Julian Börner at the heart of their defence.
"He [Lees] is a fit lad but we may give him a few more training sessions just to get him up to speed or whether he needs any Under-23s games," stated Monk. "But he is a fit lad so I doubt he needs too much.
"He is fit and well and has been back out on the pitches in the international break and we will fully integrate him after Friday."
Full-back Liam Palmer and centre-forward Atdhe Nuhiu have returned unscathed from international duty with Scotland and Kosovo respectively.
Midfielder Massimo Luongo has shrugged off the knee problem which forced him to withdraw from the Australia squad last week and is available for selection ahead of the trip to South Wales.
Monk, who says Hamburg loanee David Bates (groin) could return to training next week, said: "He [Luongo] is okay. He has been back in training this week. He picked up a little bit of a knock in the last game.
"We had to look after him in the first week of the international break but he has been fine in training this week."