The 22-year-old winger joined Plymouth Argyle on loan last summer and impressed with his performances for the League One side.
Swansea cut short Whittaker’s loan deal with Plymouth in January and recalled him back to the club amid interest from several clubs.
Michael Beale has identified him as a key target as he looks to add more attacking options to Rangers.
Rangers submitted an offer for the winger, but that was turned down by Swansea, who deemed it short of their valuation of the player.
Whittaker is keen on joining Rangers in January and the Gers are working hard on a deal to bring the winger in on deadline day.
However, it has been claimed that Swansea have opted to keep Whittaker in the January window, thwarting Rangers’ attempt to get the young player.
Swansea are currently short on numbers in the attacking area after losing Michael Obafemi to Burnley and want to utilise Whittaker for the rest of the season.