Reykjavik-based Olafur Gardarsson has so far received three offers of a new deal from Tynecastle but has yet to complete negotiations on behalf of the 19-year-old Icelander. He explained today that the situation has reached the "make or break" stage.
Jonsson's current contract runs to 2010 but Hearts are obliged to grant him an extension after he triggered an appearance clause by playing against Aberdeen in January. The club wish to secure his services until 2012 but Gardarsson is not keen for his player to sign for that length of time.
"They want Eggert to sign for four and a half years, until 2012, but I would like a shorter contract. That's one of the things we are not agreeing on," Gardarsson told the Evening News.
"The discussions are moving in the right direction but they are not finished. I received an offer on Sunday from Hearts, which was their third offer. I've discussed it with their representative, Mr Mindaugas, who I think is from the company that owns Hearts (Ukio Bankas Investment Group].
"The plan is to meet in Edinburgh next week. There are a couple of things unsolved but if we move ahead we hope to finish it next week. It's make or break now."
Gardarsson claims Hearts have yet to grant Jonsson several payments which are now overdue from his existing contract. However, the player stressed today that he is keen to remain in Edinburgh.
Jonsson said: "I'm happy at Hearts, I'm still very young and this is my first season in the first team. Hopefully I can stay here and keep improving. Obviously, you think about the contract talks off the pitch, about what's going to happen, but I still have two years left on my contract at the moment.
"We are in talks to extend that and they are going good. They probably expect me to sign a new contract some time soon."
Jonsson has been included in the full Iceland squad for next week's friendly in Slovakia and is expected to win his second international cap, recognition of his impressive form at club level this season. Gardarsson is aware he must schedule any trip to Scotland around his client's international commitments.
He added: "I will have to come over when Eggert is around so we will plan the contract talks accordingly. He is enjoying life as a footballer and making progress. He is in the Iceland national squad for next week's match with Slovakia and, in terms of football, everything is fine. We hope his new contract can be finished soon." Meanwhile, a strong Hearts reserve side went down 4-2 to Dundee United at Station Park yesterday.
Neil McCann, Jose Goncalves, Deividas Cesnauskis and Audrius Ksanavicius all featured for the Jambos, whose two goals both came from Finnish striker Juho Makela.