Newcastle believe the £10m bid that came to light on Monday was derisory - and was made in order to placate unhappy Arsenal fans who have been demanding that the club spend some money.
It is understood the prospect of Champions League football is one aspect of the move that would appeal to Cabaye.
Newcastle have no wish or desire to sell Cabaye, but just as with the transfer of Andy Carroll, a realistic bid may be given some consideration if it is in the long-term interests of the club.
Sky sources understand that Arsenal would need to offer between £18-20 million before Newcastle would be tempted to do business.
Cabaye, who moved to Tyneside from Lille in the summer of 2011, has three years left on his contract at St James' Park.
The France international had been left out of the Newcastle team which lost 4-0 at Manchester City on Monday night in the club's opening game of the season.
Speaking after the defeat at the Etihad Stadium, Alan Pardew criticised the timing of Arsenal's bid and accused their Premier League rivals of being 'disrespectful'.
"We've prepared with the lad for three days and then for him to have his head turned by this bid from Arsenal on the eve of the game is just disrespectful," Pardew told Sky Sports.
"From my view, why it couldn't have waited until tomorrow morning I do not know.
"I don't think the result would have been the same if he had played."
Pardew also believes that the concept of the transfer window needs to be addressed, with the current format leaving clubs in danger of losing key men after the season has already started.
Clubs have until 2nd September to complete their summer business this year, and Pardew feels the authorities need to look at rescheduling deadline day in order to create a fairer playing field - with Newcastle not the only side to have suffered at the hands of unwelcome speculation.
"There is a question about the window being closed before we kick off the Premier League season," he said.
"I know the Premier League asked the European leagues to do it and they wouldn't fall in line.
"But after the summer we have had, the situations we have had, with (Wayne) Rooney as well, it is definitely something they need to put under the microscope again."