The former Leeds United defender has missed the last two games with a hamstring strain, and is yet to feature under new boss Garry Monk.
“He’s on the pitches today,” said Monk. “Assessing him, he’s progressing really, really good.
“In terms of the weekend, we might be a little bit short of that but I’m hoping for next week.
“He’s edging closer every day. I said after the game on Tuesday it’s kind of a day by day thing but he’s out there today and he’s looked good and he’s looked stronger, but maybe the weekend is a little bit too soon.”
Lees could return for next Tuesday’s trip to Hull City, and after the visit of Wigan Athletic next weekend, there is a two-week international break for players to recuperate.
The Owls are stretched in defence, with summer signing Davis Bates also absent with a muscle injury.
Monk confirmed: “Batesy has tweaked a muscle. He’s not been training today, we’ll see how he is tomorrow and if he’s not quite right tomorrow then we’ll send him for a scan but we’re hoping he might be training tomorrow.
“Possibly, we’ll see, the key is to let it settle and we’ll have more information tomorrow.
“Depending on how he feels tomorrow he’ll be training, whether he’s out on the pitch or whether we need to send him for a scan.”