There are also reports that Neymar's father, who acts as his agent, has held talks with Real Madrid.
Following the recent Madrid revelations however the PSG chief has personally flown to Brazil to speak with Neymar, who is now still in his homeland recovering from an operation following the foot injury sustained during a recent win over rivals Marseille.
PSG sporting director Artero Henrique has also seemed to cast doubt on whether Neymar will stay at the club.
"He has not told me anything; but, if it's up to me, I would open the door right now", he said.
European glory is the club's ultimate aim and a main reason for their huge investment in Neymar, but they were knocked out at the last-16 stage by Real Madrid and look to be some way off being able to challenge for the European Cup.
Neymar has played 30 games for PSG so far this season, scoring 29 goals and assisting a further 19 strikes.
There is every chance Neymar may not return to Paris this season, so Al-Khelaifi has chose to travel to see him and assure the player of his ambitions for the club.