Newcastle had a bid rejected for the Lyon midfielder in January and reports have suggested that Alan Pardew has renewed his interest in the 23-year-old.
But Bernard – who started his professional career at Lyon – thinks a possible deal looks unlikely due to an apparent difference in valuation.
In addition, Bernard expects Pardew's close-season recruitment drive to be hampered by missing out on a place in either the UEFA Champions League or UEFA Europa League last term.
"For the money that's been spoken about (for Grenier), it's never going to happen," Bernard told the Evening Chronicle.
"I think if he goes, it'll be for £20 million.
"It could even be a Champions League team.
"For me it will be a surprise if he goes to Newcastle. Sadly it could be a 90 per cent no for Grenier to Newcastle."
Newcastle finished 10th in the Premier League last season after a push for the top five unravelled at the turn of the year.
Bernard added: "The problem at Newcastle has been that when the club did well and finished fifth (in 2011-12) they didn't invest.
"Now it's a whole lot harder for them to attract players.
"We have not done well enough to attract some of the ambitious players. They want to see a club playing in the Champions League or even the Europa League.
"And Newcastle aren't close to that at the moment. I really think the Grenier deal is unlikely."
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