The Magpies boss will send out his side for their first pre-season friendly at Darlington tomorrow night with both men entering the final year of their contracts.
Barton has been told he will not be offered a new deal, while Enrique is in no hurry to reach an agreement despite being presented with a package described by Pardew as 'one of the best offers we have ever made a player'.
Gunner get ya! Enrique is being tracked by Arsenal
However, with no bid yet on the table for either man, the manager will simply get on with the task of making sure his team is ready for Arsenal's opening day trip to St James' Park.
Pardew said: 'The situation is simple: if players don't want to commit to contracts or this is not the contract offer that they wish, there's not much you can do about it.
'But we have a good feeling in the dressing room, we are looking forward to the season and I think we have got a decent side this year.'
Barton's situation is somewhat different to that of Enrique with the club having withdrawn the offer they tabled in January after the contract went unsigned.
Home boy: Barton has been left behind as the club travel to the USA
But Pardew remains as relaxed as he can be over a player who has repeatedly vowed to see out his current deal.
The manager said: 'We are at a situation where we will play this season as it comes and we will all sit down at the end of the year, and who knows? We might do a deal then.
'You never know in this game. It's a strange business we are in. He's a good player, he's playing well for us and that's all I care about.'
Barton, of course, will not travel with the rest of the squad to the United States on Sunday after being refused an entry visa, but Pardew is confident the 28-year-old will make his presence felt with the reserves in Holland before linking up with his senior team-mates once again on their return.
He said: 'He's a very important player for us and the example he sets with that group will be first-class. I am looking forward to seeing him when I come back and getting him ingrained in the team.'
Pardew is continuing his search for a striker - Paris St Germain's Mevlut Erding remains in the frame - and insisting that the ?35million the club received from Liverpool for Andy Carroll will be reinvested, although not necessarily in transfer fees alone.
But he has admitted Charles N'Zogbia and Neil Taylor are unlikely to arrive on Tyneside, and had to fend off claims that Chelsea could make a move for Ivory Coast midfielder Cheick Tiote.
Pardew said: 'He's a great player who had a great first year for Newcastle. We have heard nothing substantial. The information that we have had about this is purely speculation.' CLICK HERE TO SIGN UP FOR OUR FREE FANTASY FOOTBALL GAMEArsenal set to launch bid for Newcastle defender Enrique as Clichy's replacementSol Campbell training with Arsenal as veteran defender seeks a new clubAll the latest Newcastle news, features and opinion