Pardew insists the problems exist between Barton and the board, and he would welcome a player of his ability back into the squad if the situtation can be resolved.
Barton has made no effort to hide his anger at the way the club is being run. On Monday he was placed on the transfer list for free and then forced to train on his own.
On Thursday he was back training that the club, but only allowed to join in with the youth squad rather than the first team.
"I've never closed the door on anyone and I'm not closing the door on Joey," Pardew told a press conference. "He trained with the development team today and, who knows, he may train with the first-team soon."
Moments later Barton said on Twitter: "Does anybody have Isambard Kingdom Brunel's number?" This was a reference to the 19th century British civil engineer and bridge builder.
Pardew is understandably reluctant to allow a player of Barton's stature to simply leave after he was a key figure as the Magpies comfortably remained in the top flight following promotion last term.
The former West Ham boss is hopeful a resolution can be found with the Magpies' home opener against Arsenal - a club linked with Barton - just 10 days away, although he stressed the midfielder would need to show some contrition.
Pardew continued: "It's a situation I didn't envisage being in. Joey is a great player and you want great players in your team. It's very important as a football club that you are all pulling in the same direction - at this moment of time where Joey is not pulling in the same direction.
"That's not to say that can't change in a short period of time. I'm still reflecting on the situation, as is Joey at this present time, on how best to resolve this issue. I think that is important at the moment.
"Maybe if it wasn't for Twitter and this instant media it may have got resolved on Monday morning with me and Joey in my office. The problem with Twitter - we need to get a hold of this. We have got nothing from the Premier League on how to deal with this."
The Magpies boss has even called for the counsel of Manchester United boss Sir Alex Ferguson on the subject, as he looks to provide a guideline to direct his players' use of the website.
"I spoke with Sir Alex Ferguson today and he's had this problem with Twitter before," he added. "You cannot be critical of the club within a personal account. You shouldn't do that on your own account.
"We're now following the guide that Sir Alex has said they have done (at Manchester United). I'm not against those sites, and I don't think many managers in the Premier League are, but they have to be careful not to mention the football club.
"It's obvious we need to resolve the Joey situation. We also need to bring some players into this club. We need a signing or two. I haven't even considered that (Barton's replacement). Like I said, it is a time for reflection.''
Two players who look set to leave the club, however, are Jose Enrique and Wayne Routledge. Pardew expects full-back Enrique to play in Saturday's friendly against Fiorentina, despite being strongly linked with Liverpool, while Routledge looks closer to finalising a move to Swansea.
"Enrique is still here and will play on Saturday," he added. "I don't see issue that he won't start. I know there's interest in Jose, but no concrete interest. We are poised to react to that. As for Wayne I'm not sure if that deal is finalised but I believe it is very close."
Newcastle have issued a statement which says neither the club nor Joey Barton will make any further public comment on the player's future. It remains to be seen if Barton is able to stay within the boundaries of that truce on his Twitter account.
"We understand the level of interest in the club's decision to offer Joey Barton a free transfer,'' the statement read. ''However, it would not be dignified, nor would it serve any useful purpose at this present time, for either the club or Joey to air their private issues on this matter in public.
"The club and the player have important business to focus on over the coming days and both parties have come to an agreement that we will not comment further at this time."