The Canaries, as well as Sunday's opponents Wolverhampton Wanderers and newly promoted Sheffield United, are said to be interested in the 23-year-old former Watford man.
While Rangers might be loathe to lose one of their more promising talents, their caretaker boss Gary Waddock is realistic about the financial situation at the club.
"I will not want to let him go because he is a quality player,” admitted Waddock. “But we all know the financial situation of the football club and if a big offer does come in for Lee Cook then money does talk.”
Worthington was linked with Rs defender Danny Shittu in January, and could return with a bid in the summer. Cook, on the other hand, is a left winger, and it is widely believed that City's priorities will be a target man striker and a right winger.