Rose has not been involved with the Spurs first team squad this season after being frozen out by Jose Mourinho.
The 30-year-old was left out of Tottenham's Premier League and Europa League squads this season.
Rose, who is the club's longest serving player, went out on loan to Newcastle in January last season following a heated meeting with Mourinho, all of which were caught by Amazon's All or Nothing cameras.
It seems that his contract could be cancelled this month with West Brom keen to sign him.
Speaking on White and Jordan on talkSPORT, Crook said: "I was told there was a big chance he could follow Jack Wilshere in the sense that Tottenham could cancel his contract in this window.
"We know he's not part of Jose Mourinho's plans.
"West Brom and Sam Allardyce would be very keen to take him to the Hawthorns - whether he would see that as the right club to revive his career, I don't know."
"I can understand why Big Sam would want him, he's desperate to bring in some Premier League experience, added Crook.
"But like Wilshere and like Mesut Ozil at Arsenal as well, the time has come for Danny Rose to put his football aspirations ahead of his pay cheque and just get some minutes under his belt.
"This career doesn't last forever, and at the moment he's just rotting at Tottenham."
Tottenham could cancel Danny Rose's contract during the January transfer window, according to talkSPORT's transfer expert Alex Crook.