Benitez has endured a hard relationship with the club's owner Mike Ashley, with the former Liverpool and Real Madrid boss wanting assurances over the club's ambition before making a decision on his long-term future.
The travelling Newcastle fans led chants about wanting Benitez to stay throughout Sunday's game but, ahead of discussions, the ex-Liverpool boss gave no indication over whether he will remain at St James' Park.
Celtic know themselves that bringing a high calibre manager in on big wages will mean they would also have to offer a big budget and that's something the club wouldn't even do for Brendan Rodgers.More news: Sri Lanka clashes kill one; imposes nationwide curfew after mosques attacked
"If we have a meeting at the end of the season, you know the owner has to be around", said Benitez, whose contract expires at the end of June.
"It's important, as players, we had someone like that". My opinion is a mix of both, however, I do think Newcastle could have done more in some games and at least hit the 50-point mark.
"We just need to build a culture here and a mentality so what happened today doesn't happen [again]", Parker told Sky Sports.More news: Schiff: Campaigns Shouldn’t Be Allowed to Get Foreign Help
"Hopefully he can stay and we can continue to create a good team, and look forward to the future with hope".
"We've waited 8 months, so we can wait another 10 days".
"When a team gets relegated, teams want to come for your best players, we'll no doubt have that problem".More news: Barr Orders Connecticut Prosecutor to Investigate Mueller Probe
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