The Senegal Football Federation are understood to have threatened to invoke FIFA's five-day rule, which would prevent Cisse lining up against the Welshmen after failing to report for duty for their friendly against Niger in midweek.
However, the Magpies insist they kept the African nation's football chiefs fully informed of the 27-year-old's situation after he was unable to play the second half of last Sunday's 1-0 home defeat by West Ham because of a back problem.
Manager Alan Pardew said: "Papiss, we have a bit of an issue going on at the moment with the federation.
"We feel we have covered all the bases to give them the information, but they seem not to have received it, so we are in discussions with Senegal and the FA about his availability for Saturday.
"We gave a report and an e-mail straight after the game that at half-time, he was feeling his back and we took him off the pitch. We also sent reports of the injury, or the doctor did.
"We didn't, as far as I'm aware, get too much information back, and now it seems that Senegal are upset that he didn't appear for them.
"Somewhere along the line, there has been something lost in translation here, so we are trying to sort that out today [Thursday] and hopefully, it will be clear for Papiss to play and Saturday and clear for him to continue for Senegal going forward, because I don't think anyone wants bad feeling."
Pardew could do without losing his £9million frontman as he prepares to head into battle with the Swans already without a series of senior players.
Skipper Fabricio Coloccini serves the second of this three-game ban following his sending off at Liverpool, and he will be joined on the sidelines by Jonas Gutierrez and Yohan Cabaye.
Gutierrez injured a knee against the Hammers, and while the damage is not as bad as was first feared, he will not be risked this weekend, while Cabaye has been ruled out by the groin problem which prevented him from playing in France's friendly against Italy.
Pardew said: "Cabaye didn't play for France and it doesn't look like he's going to play for us at the weekend.
"With Jonas, it's actually better than we thought. Sometimes the player gives better information than the scan, and he feels good about it.
"But we are going to be cautious with it because we don't want to take a risk and then lose him for a considerable amount of time, so I think this week, he will miss the game.
"But I think there's a good chance he could play at Southampton (next Sunday)."
In the circumstances, midfielder Cheick Tiote's return from suspension - he was sent off during the 1-1 derby draw at Sunderland on October 21, and will sit out next Thursday night's Europa League clash with Maritimo after reaching three bookings in the competition - is all the more welcome.
Pardew said: "He's a massive part of this club and this team's success over the last couple of years. He's a massive player for us.
"This year, perhaps, he hasn't been at his best, but he has had no rhythm in terms of playing games.
"He got injured, then the suspension, so we are really hoping he gets a run now right up until the African Nations and he is back to his best. He's very important to us."