The former England Under 21 star is very much in demand, with a host of Premier League clubs battling for his signature.
Bolton were leading the chase as they targeted him to fill the void should Gary Cahill complete his move away.
But, while Cahill remains at the Reebok Stadium, Bolton can't make their move, which has now seen other clubs come in.
According to skysports.com, both QPR and Wolves have now made offers believed to be in the region of £2.5million for the 25-year-old stopper.
West Brom are also in the mix, but they are believed to be looking at a loan with a view to a permanent deal.
North East duo Newcastle and Sunderland are also monitoring the situation but City are hoping a deal is concluded sooner rather than later.
City boss Roberto Mancini has told Onuoha, who came through the club's own youth system, that he does not figure in his plans.