Al Khelaifi has moved to ease the tension between the pair after their spotkick bust-up against Lyon.
El Pais says Al-Khelaifa instructed an intermediary to offer Cavani an improved contract in exchange for allowing former Barcelona star Neymar to take the penalties.
The Uruguayan forward was offered one million euros if he finishes the season as the PSG's leading goal-scorer in Ligue 1. That clause was not previously in his contract. Cavani, who has scored seven goals in seven league matches so far this season, rejected the offer.
Unai Emery and sporting director Antero Henrique have been working with club captains, Thiago Motta and Thiago Silva, to reconcile differences. Neymar's reported apology has done little to repair damaged relationships.