The Magpies signalled their intention to make the 25-year-old Spaniard a "fantastic" contract offer to keep him at St James' Park, with his existing terms due to expire at the end of next season.
Enrique has been repeatedly linked with a move away from Tyneside this summer with the Reds and Bayern Munich among those clubs understood to be monitoring his situation.
Pardew has revealed there has been little contact with the player or his camp since the end of last season as Newcastle prepare to implement their plans for the new campaign.
He told the Evening Chronicle: "At the moment, it looks like he doesn't want to deal with us.
"We have been asked to make him an offer, but there has been no progress since then. I still hope we can do something but at the moment, we are still waiting for Jose.
"I don't think there's anything more I can really add on that situation at this stage."
Pardew made the retention of Enrique and key midfielders Kevin Nolan and Joey Barton his first priority in the wake of the club's successful bid to secure its Premier League status.
However, his plans look to be in tatters with the wall of silence surrounding Enrique, skipper Nolan having rejected the offer currently on the table and Barton having been told he will not be handed a new deal.
Enrique and Barton each have 12 months remaining on their current contracts, while Nolan has two years, although uncertainty now surrounds all three.
The Magpies have rejected a "derisory" offer from West Ham for Nolan - understood to amount to just £1.5million for a player who scored 12 Premier League goals last season - and although Barton has vowed to see out his contract at St James', there is also interest in him.
Pardew last week snapped up Lille midfielder Yohan Cabaye and is hopeful of completing a swoop for Swansea left-back Neil Taylor, although he is not seen as a direct replacement for Enrique should he move on.
But efforts are continuing elsewhere to boost the squad with a replacement for striker Andy Carroll a priority.
Newcastle have held an interest in West Ham's Demba Ba for some time and having missed out on Lorient frontman Kevin Gameiro when he opted to sign instead for Paris St Germain, are considering their options on that front.
Pardew said: "Things are definitely moving on now and we expect to be busier between now and the start of the season.
"We are working very hard on one or two players and we hope to announce something soon.
"We should be able to announce a second signing, I would think, in the next 10 days."