Reports north of the border suggested that the Millers tabled a £375,000 offer for the highly-rated 23-year-old as they bid to prize him away from Easter Road.
But Hibs insist no official bid has been made by the Millers, though talks over a fee for Allan are thought to be at an advanced stage.
Allan, who has been a summer-long target for Rangers, submitted a transfer request last week after two bids from the Ibrox club were rejected.
Mark Warburton's men entered a third bid on Tuesday night, believed to be an improvement on previous £175,000 and £225,000 advances, but Hibs are refusing to sell to a rival club who they are going head-to-head with in the Scottish Championship this season.
Millers boss Steve Evans, who often targets players from his native Scotland, is believed to be keen on Allan and hopes to take advantage of the Edinburgh club's refusal to do business with Rangers.
He may have to ask chairman Tony Stewart to dig deep, though, as they work hard to agree a fee.
Allan, who has had spells in England with West Brom, Portsmouth, MK Dons and Birmingham, joined Hibs from the Baggies last season and has made 44 appearances, including two this season.
On Saturday, Evans revealed the Millers were in dialogue with another club over a permanent transfer.
Rotherham have made 11 summer signings so far, with the 2015/16 season kicking off against MK Dons on Saturday.
