The Ivory Coast international missed Sunday's 2-2 draw against Burnley with a muscle injury picked up in the Boxing Day win over West Brom at The Hawthorns.
With City boss Manuel Pellegrini without the likes of Sergio Aguero, Edin Dzeko and Vincent Kompany, his squad would be stretched further by a long-term lay-off for Toure.
The Chilean revealed that it would have been a risk to play Toure against Burnley and confirmed the club will assess him further on Monday.
"Yaya Toure was not able to play 90 minutes [against Burnley]. It was a risk, he can do it [but] maybe it was a risk for him," he said.
"The players that played [against Burnley] were the players that were able to do it.
"Yaya felt a problem at the beginning of the last game against West Brom, he was not 100 per cent recuperated. I think that it was not good for him to play.
"We will see [if he is available for Sunderland], we hope that he will be because it was a less problem, but after 48 hours maybe it's too high-risk injury to repeat."
Pellegrini had stated on Friday that Kompany could return from a hamstring problem in time for Sunday's visit of Burnley.
However, the skipper was not risked and Pellegrini explained he too is doubtful for Thursday's clash with Sunderland.
"We'll see if he's fit for the next game," Pellegrini explained.
"It's very difficult for now to know because he still has some problem in his calf."
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