Negotiations for a new deal between the club and midfielder have been going on since last year as his contract expires in June.
According to a source close to the player, Ekstein is unhappy with what the Naturena-based side has put on the table, and might soon sign a pre-contract with one of the club's rivals.
"Pule's contract is coming to an end at Chiefs in June," the source tells snl24.com/kickoff.
"And the contract that Chiefs is putting forward is not what the boy expected. Now there are teams already that are talking to him on the side offering him a better contract which is way better than what Chiefs is offering. What Chiefs is offering him is very little you see. The club is willing to renew his contract, but the thing is the money is not okay.
"I can tell you the likes of SuperSport, Wits and Pirates are interested ... especially Pirates. Chiefs want to give him only two years, while the other teams are talking three years and serious money."
Asked for comment, the club's communications manager Vina Maphosa says he is in the dark over such matters.
"I don't have any feedback on my table regarding that. And how we work at Kaizer Chiefs I'm sure you know. When we do a wrap of the window period and all that, we also clarify on contracts, and that will be the end of the month."
Asked further if the negotiations between the player and the club have at least started, he says: "I don't know. I don't go to football management to find out who are they discussing with who. They give me a report at the end, 'that we were discussing with this one, we didn't agree. Or we are discussing with this one, this is the progress. We are signing this one or we were trying to sign this one, this is what happened blah, blah, blah'. So we don't do it in pieces anytime one, one, one ... no. At Chiefs we don't do that."
The 28-year-old has featured 15 times for Amakhosi this season in all competitions, scoring two goals and providing a single assist.