Napoli president Aurelio De Laurentiis has entered talks with the players over their bitter stand-off.
After refusing to return to ritiro a fortnight ago, De Laurentiis handed a series of fines by scale.
Allan was reportedly being penalised the most - 350,000.
Tuttosport says he met privately with Allan, Lorenzo Insigne and Dries Mertens, as they were viewed as the chief instigators in the situation.
Allan was told his fine was heavy due to his disagreement with Edo De Laurentiis, Aurelio's son and the vice-president.
Insigne meanwhile, was fined because as captain, he didn't follow orders and return to Castelvolturno, where the club's ritiro was.
It's suggested the president would be willing to suspend or reduce the fines if Napoli beat Genk and reach the Champions League Round of 16.
