The 31-year-old Norwegian has barely featured this season under new boss Gerard Houllier, while a torn calf muscle has resulted in an enforced spell on the sidelines.
However, Carew, who has scored 52 goals in 132 appearances since joining the Villans four years ago, has been attracting the interest of several clubs when it became clear that Houllier would be looking to offload him when the New Year transfer window opens for business.
Vila's deadly rivals Birmingham were linked to Carew, while Fulham are another side whose boss Mark Hughes was said to be wanting Carew to ease his striker problems at Craven Cottage.
However Villa's Midlands rivals West Brom appear set to win the race with Carew reportedly set to join the Baggies in a deal worth around £1million.
Villa will then use the money to help in their bid to strengthen with Tottenham's Robbie Keane and Pablo Osvaldo of Espanyol thought to be top of Houllier's wanted list.