The club confirmed today that Cole, who is out of contract in the summer, needed more surgery on a knee ligament injury that has failed to mend after the first operation.
The 33-year-old Cole scored 10 goals in 22 starts before getting injured in February to earn the offer of a one-year extension and Pearce has confirmed it still stands.
"There is a deal on the table for Andy and we will keep to our word on that," said the City chief. "He has been an important member of our squad this season and a big miss over the last few games.
"You know he will convert a high percentage of the chances he gets and he scored 9 goals for us in a very short space of time. But he had an operation a few weeks ago which wasn't settling down as we would have liked, so he needed another minor operation.
"With the season running down, it is highly unlikely we will get him on the pitch again this year."
With 10 City players now out injured, Pearce is down to just 13 senior players, but he stands by his decision to let Robbie Fowler rejoin Liverpool in January.
"The business regarding Robbie was very good," said Pearce. "It's very easy at any given moment to say 'let's stop the clock' but life doesn't work like that.
"Letting Robbie go back to Liverpool was the right move for him and the right move for us because it allowed us to get Georgios Samaras in."
Cole, Onuoha and Jordan are out for the season, and although Samaras, Sibierski, Sinclair, Barton, Reyna and Riera are all carrying minor knocks, they're not expected to be available again until we play Tottenham on April 8.
At Chelsea on Saturday, Sommeil therefore be pushed forward into a midfield holding role, while young quartet Matthew Mills, Ishmael Miller, Ashley Grimes and Marc Laird could all be named in the squad.