Allan, 23, who has a year remaining on his current Hibs contract, has also been linked with Celtic and his former club Dundee United.
The reported approach from Rangers comes only three days before the teams meet in the first round of the Petrofac Training Cup.
New Rangers boss Mark Warburton was at East End Park at the weekend when the 23-year-old scored a spectacular opener against Dunfermline.
Last season’s Championship player of the year returned to Scotland last summer on a two-year contract after falling out of favour at West Brom.
He rediscovered his form with the Edinburgh club and recently paid credit to Hibs manager Alan Stubbs.
“Obviously after my experience down south I have taken on board why I wasn’t playing and I feel I have put that right this year,” Allan said in May.
“I have managed to kick on and, like I say, Stubbsy has given me that platform to go and play.
“I needed a manager to have faith in me and know my strengths. And Alan Stubbs has been that for me.”