Sky Sources revealed on Wednesday that Rangers had an offer rejected for the 23-year-old midfielder, who has a year left on his contract at Easter Road.
And Hibernian boss Stubbs claims the £175,000 offered for last year’s Championship player of the year is almost insulting.
“It doesn’t say a lot for what Rangers think of the player, I think that’s probably the best way to put it,” said the former Celtic and Everton defender.
“You can’t stop bids coming in, the transfer window is open. But we’re not welcoming any bids. Our position hasn’t changed from when I spoke about it a month ago so that’s the situation.”
The offer from the Ibrox club came just days before the two sides are due to meet in the Petrofac Training Cup at Easter Road.
“I’m not surprised by the timing at all,” added Stubbs. “We as a club will deal with it the way we have done.
“It’s exactly the same as what I said six weeks ago. We as a club are willing to let Scott Allan have his contract run down this year so as far as we are concerned our stance hasn’t changed one bit.
“Scott’s a big part of our plans to put a team together to reach our aims this season. Why would we want to lose one of our best players?”
“I’ve got a really good relationship with Scotty. He’s been kept addressed of everything that’s happening. So it will be no different this morning. We’ll be preparing for the season with Scott Allan.”
And Hibernian chief executive Leeann Dempster fully backed her manager claiming it was “an easy bid to reject”.
“Scott Allan is one of Scotland’s best midfield talents and last season’s Championship player of the year, and any approaches for him are unwelcome,” she said.
The Easter Road side came out victorious in four of the seven matches between the clubs last season, but lost out to Rangers in the end of season play-offs.
Rangers manager Mark Warburton has been in his role just over a month but Stubbs says he can already see big changes from last season’s squad.
“I saw them on Tuesday and they’re trying to play the ball around more and a more passing game,” he said. “It will be a good game of football because that’s something we want to do as well.
“As far as I’m concerned it’s a competitive game and every competitive game we play in we want to win. It’s the first game in front of our fans at home. Our intentions are, whether it’s a cup game or a league game, we want to win the game.”