The 29-year-old centre-back has fallen out of favour at Stamford Bridge this season and submitted a transfer request before Christmas which was accepted by the Blues.
Andre Villas-Boas has asked him to train with the reserves and decided against a recall even when Chelsea were struggling with injuries.
With Gary Cahill's arrival from Bolton expected to be confirmed in the very near future, Alex is very much surplus to requirements and has been linked with a number of other clubs.
He had been linked with QPR earlier this month when Neil Warnock was still in charge, and it appears a move to Loftus Road could still go ahead.
With new manager Mark Hughes currently assessing his squad after taking charge on Tuesday, it is understood an offer has been made for Alex, according to Sky Sports sources.
QPR owner Tony Fernandes revealed on Wednesday that he was ready to spend money in the transfer market and hoped to sign somebody before the weekend match against Newcastle.
It seems that new arrival could now be Alex, who has proven his Premier League credentials at Chelsea since a loan spell with PSV Eindhoven came to an end in 2007.
