The disgruntled Roosters star is believed to have been shopped around to interested NRL clubs as the Roosters attempt to keep their grand final roster together while building the club around young halves Todd Carney and Mitchell Pearce.
Parramatta have reportedly already knocked back an offer for Anasta, who has one year to run on his contract, to join the Eels for 2011.
In September last year Cowboys skipper Johnathan Thurston begged the club to “throw the cheque book at (Anasta)” in a bid to reunite the former Bulldogs teammates.
But it appears Thurston’s request has fallen on deaf ears, with Cowboys football manager Peter Parr said the club had no intentions of re-opening negotiations.
Regardless of Anasta’s availability, Parr said the Townsville-based team were not in a position to put an offer to the former Australian and NSW representative after going on a significant spending spree that has netted Brent Tate, Dallas Johnson, Ashton Sims and Glenn Hall.