Blues boss Andre Villas-Boas confirmed on Thursday the club had received an offer from a Premier League rival for the defender and implied the bid fell short of their valuation.
QPR are believed to be the club chasing Alex after new manager Mark Hughes set his sights on the Brazilian.
And it is thought the Hoops have now lodged a second bid as they push to make their first signing under Hughes.
Centre-back Alex wants to depart Stamford Bridge this month and saw a transfer request accepted by the club in December.
He no longer features in Villas-Boas' plans, with Chelsea closing on the signing of Bolton stopper Gary Cahill.