Lyon rejected Newcastle's initial bid of around £8m yesterday, but talks are ongoing as the Magpies look to secure a replacement for Yohan Cabaye.
French sources claim there is unlikely to be any agreement unless Newcastle increase their offer to at least £12m, and it remains to be seen whether Mike Ashley will be willing to sanction such a high outlay on a relatively unproven 23-year-old.
However, Pardew is hoping there is a breakthrough in the final two days of the transfer window, having admitted his squad will be weakened if Cabaye is not replaced.
When asked whether there was any update on the Grenier situation, he said: “Not in terms of whether the deal is finalised or finished. It's ongoing as far as I'm aware.
“There's two days left and we'll have to wait and see. We're hopeful, but that's where we sit today. He has tremendous technical ability, and is a player our fans would love to see at the football club. But he's still not our player.
“You can't take a player like Cabaye out and say it's not going to weaken you. It is unless you can replace him like for like, but whether we can do that, I don't know.”
Newcastle completed one signing yesterday with Luuk de Jong arriving on loan from Borussia Monchengladbach, but Pardew does not envisage the striker going straight into the starting line-up against Sunderland.
“He's a player we had our eye on for a while, but couldn't quite reach in last window. It didn't really work out (at Monchengladbach), and he's ended up here. He's trained well and we're looking forward to his inclusion in the squad.
“But he hasn't had much game action and this is the Premier League. I would suggest that I might be a better judge (about him starting) than he is, but I like his confidence and he's trained very well.”