The 23-year-old is also said to be on Aberdeen's radar, as Hibs fight to keep the midfielder from a move to Ibrox.
Hibernian midfielder Scott Allan has handed in a written transfer request, the Edinburgh club have confirmed on their website, with Rangers continuing to pursue the 23-year-old as they have for much of this summer.
The 23-year-old's future is far from certain though, as Hibs have made it clear that they would not be selling the player to a direct rival in the Scottish Championship.
The club's website issued the following statement regarding Rangers interest in the player, with the last sentence printed in bold to emphasise the point as part of the statement:
"In the face of continued media interest, Hibernian Football Club can confirm that Scott Allan has today handed in a written transfer request.
"This comes on the back of two unwelcome and uninvited approaches from Rangers FC regarding Scott, the first for £175,000 and the second for £225,000.
"Hibernian FC has refused both bids because the Club has no wish to transfer a valuable player to strengthen a major rival in the battle to win the Championship and gain promotion to the Premiership.
"Hibernian’s position has not changed. The player will not be sold to Rangers."
On top of that, there are reports that Aberdeen are interested in the player in the Press and Journal, a possible solution to Allan's desire to leave Easter Road without heading to Ibrox.
It wouldn't be much of a solution for Rangers though, who have already had two bids rejected for the former West Brom and Dundee United man and would be desperately disappointed to see him sold to another club this summer.
Mark Warburton should take heart from Derek McInnes's comments that he isn't interested in the player, with the Dons manager being quoted as telling the Press and Journal that "Scott Allan is not a player that we are pursuing.”
Allan made 42 appearances for Hibs last season, and seems to be at the centre of an almighty tug of war between the two clubs desperate to escape from the Scottish Championship in the coming season.
Whether Rangers can offer a substantial enough compensation package to convince their divisional rivals to sell remains to be seen, but right now, it looks like the Cabbage are really digging their heels in.