PSG won the race to land Ekitike last summer, seeing off competition from Newcastle United and splashing €35m to sign him from Reims.
However, the 21-year-old has struggled to make an impact in the French capital and could move on this summer.
Everton, looking for attacking reinforcements, are interested in signing the striker and have now made their move to take him to Goodison Park.
The Premier League side have gone in with a bid for Ekitike which PSG are now considering.
Everton will wait to see if the offer they have presented to PSG is enough to be accepted.
Ekitike made 25 appearances in Ligue 1 for PSG over the course of last season and hit the back of the net only three times.
His chances of regular game time may be limited if he remains at the Parc des Princes into the new season.
