The 27-year-old's future at Craven Park is understood to be in the balance after coach Justin Morgan claimed he was 'not fit for selection' for last Friday's clash with Catalans.
Salford coach Shaun McRae worked with Cooke during their time together at Hull FC and had indicated in the recent past that he would be interested in signing the England international.
But the Reds football director Steve Simms told the Manchester Evening News: "Cooke is a good player but as a club he doesn't interest us and we don't want him.
"We have other options open to us at half-back. Cooke won't be coming to Salford.