The 29-year-old had been with Rangers in recent weeks and Ally McCoist's side offered him terms to remain in Scotland.
However, interest from England has seen the Lithuanian shun a move to Ibrox and he has been lured south of the border - QPR in pole position as he is already training with Harry Redknapp's side.
But Sky Sports understands that a number of Championship sides including the likes of Leeds, Middlesbrough, Birmingham and Blackburn are all monitoring the situation.
His representative Barry Hughes confirmed that Zaliukas was now in England.
"I can confirm that Marius is training with QPR," Hughes told Sky Sports.
"I can't say anything about any other interest, other than there has been a number of clubs make contact."