"If I could get a four-year deal on the table I would snap their hand off," Jones told the South Wales Evening Post.
"That would take me to the next World Cup.
"I have had offers from everywhere but staying with the Ospreys would be ideal.
"I am an Ospreys boy. I enjoy life here and the future at the region is bright with the young kids coming through.
"I hope I can remain here but I will see how it goes over the next couple of weeks. Hopefully, it will be sorted. I would like my heart to rule my head on this decision."
The Ospreys saw Lions trio Mike Phillips, James Hook and Lee Byrne all leave for France last summer, while fellow Welsh stars Luke Charteris and Gethin Jenkins could be heading to the Top 14 at the end of the current season.
The introduction of a salary cap for the four Welsh regions has sparked rumours of a mass exodus from the Principality as the Ospreys, Blues, Dragons and Scarlets look to cut their cloth according in tough times.
And Jones, who is widely regarded as one of the world's leading tight heads, admits France will be his destination if he doesn't reach an agreement with the Ospreys.
"I want to stay but if the Ospreys don't want me then I am going to have to go," added Jones.
"A lot of stuff has happened recently because of the salary cap issue. It is a case of the Ospreys Board getting the finance stuff sorted.
"It's a hard situation and you can understand both sides. You have teams relying on tighter budgets but players out of contract have to do the best for themselves.
"I have had offers from everywhere. There is more money on offer in France and it is stupid money.
"The region have shown nothing but support but, if we don't come to an arrangement and I have to leave, France will be the first place I go."