Bell, 29, joined Rangers from Kilmarnock back in 2013, but has endured an injury-hit time at Ibrox, before blunders in the play-offs led to fans turning against him.
When Warburton was appointed Rangers boss over the summer, he almost immediately swooped to sign goalkeeper Wes Foderingham on a free transfer from Swindon Town, effectively demoting Bell to second choice.
Foderingham has been the No. 1 throughout the season, but Bell's situation has worsened this month, as Warburton has brought in another goalkeeper, with Polish stopper Maciej Gostomski signing a six-month contract after leaving Lech Poznan.
Bell's contract expires in 18 months, and his future is currently looking bleak after the signings of Foderingham and Gostomski - but he has surprisingly been blocked from leaving Ibrox.
The Scottish Sun report that rivals Aberdeen wanted to sign Bell this month having seen their loan goalkeeper Danny Ward return to Liverpool, and the player was keen on the move so he could play first-team football at Pittodrie.
However, it's stated that Rangers boss Warburton has blocked the move, leaving Bell 'frustrated' with his situation at Ibrox, especially given that it's unclear just why he hasn't been allowed to join Aberdeen.
Warburton may want experience around new signing Gostomski or just want three goalkeepers around the squad having loaned Liam Kelly out to East Fifre last week, but it seems that Bell won't be allowed to leave Rangers this month, despite seemingly being third choice goalkeeper at Ibrox.