The 32-year-old former Manchester United man was due to have scans to assess the damage he suffered during the 3-2 Peace Cup victory over Groningen at the weekend following the Black Cats' return to England.
Manager Martin O'Neill initially feared one of his most experienced players could be sidelined for months, but he was more optimistic on Thursday as he awaited the results of the medical tests. O'Neill said: "He will be assessed today. He is doing some scans and I'm hoping that the news is going to be okay. But his knee is really swollen."
O'Neill revealed the decision to give 28-year-old Turner permission to talk to Norwich was taken before misfortune struck Brown. The former Hull defender was in East Anglia on Wednesday for a medical and to thrash out the fine details of the proposed move.
O'Neill said: "Norwich had asked us about it before Wes' injury and so having given permission for Michael to go down there and the clubs having agreed a fee, it was just ironic that Wes got injured at the time.
"We will see what develops down in Norwich, but I am hoping that Wes' injury is not as bad as it might have been. But we do have a number of centre-halves at the football club at the moment, and priorities in strengthening are probably elsewhere."
O'Neill has made little secret of his intention to add attacking players to the squad this summer with strikers Asamoah Gyan and Nicklas Bendtner having departed, the latter after a loan spell at the Stadium of Light.
However, while he has been repeatedly linked with the likes of Wolves' Steven Fletcher, Wolfsburg's Patrick Helmes and Gabriel Agbonlahor, a player with whom he worked at Aston Villa, the Ulsterman was giving little away.
He said: "There hasn't been a phenomenal amount of movement in the transfer market. That doesn't really matter, I'm not too concerned with what other clubs are doing.
"We have an eye on one or two players and we are hoping to be able to do something. We all know what's needed at the football club and I will do my very best to ensure that happens. We have a number of things that we are moving on at the moment. They tend to drag on a little bit, that seems to be the nature of things."
Source: PA
Source: PA