The 29-year-old has been out injured for much of this season, and is looking for a short-term loan move to get some first-team football to his name.
Wes Foderingham and Maciej Gostomski are ahead of him in the pecking order at Ibrox, and it is stated in the report that Aberdeen made a loan swoop for Bell on Monday, with the Dons looking to sign a replacement for Danny Ward - who has been recalled by Liverpool.
Mark Warburton rejected the approach, despite Bell not likely to feature for the rest of this campaign, and the report claims that Bell himself held talks with Warburton yesterday to discuss his future.
It is stated that Bell urged Warburton to reconsider the rejection of the loan, and allow him to join the Dons for the rest of the season.
There is no indication in the report as to how Warburton reacted to the talks, although there has still been no offer accepted by the Gers to send Bell to Aberdeen.