The Citezens are on the lookout for a new boss following the departure of Kevin Keegan last week and Allardyce was one of the names touted for the hotseat at the City of Manchester Stadium.
Allardyce has today taken himself out of the running and has instead decided to concentrate on the job he has to do at Bolton which is to aim for a European place.
Earlier on in the season the former Notts County and Blackpool manager had rejected the chance to take over from Sir Bobby Robson at Newcastle United and is now doing likewise with City.
"I heard the Manchester City chairman and he said he has appointed a manager and that man is Stuart Pearce, I've too much going on here to think about the Manchester City situation."
"I just want to concentrate on Bolton finishing the highest they have ever done and getting into Europe through the only route we have now, which is through the league. Then we'll see what happens in the summer in terms of what we have to build on and whether we are in Europe or not."
Former England and Nottingham Forest defender Pearce has been appointed as City manager until the end of the season by their Chairman John Wardle and could be set for a more permanent arrangement should he make an impression.