According to TMZ, Rosengart offered to end the dispute for around US$7 million (NZ$11.6m), but reached an impasse when he declined to explained to Tri Star and Jamie's teams as to how he had arrived at that figure.
Rosengart has previously claimed the singer's father and the company misappropriated massive amounts of money from the star which could contribute to the large settlement sum.
However, both stars are still open to settling and a source told the outlet that as recently as this week, the lawyer contacted Tri Star to press ahead with a possible settlement, though the exact amount remains a sticking point.
In July, a judge ruled that the Gimme More singer won't have to sit for a deposition because it is "unlikely to provide any discoverable information".
Judge Brenda Penny said: "There exist alternative and less burdensome means to seek information."
The pop icon's lawyer praised the ruling at the time.
He said: "We are very pleased, but not surprised, that Judge Penny reconfirmed her thoughtful and legally correct ruling, once again rejecting Mr Spears's shameful and desperate effort to take his own daughter's deposition.
"Any decent man, especially father, would accept his losses and simply move on."
Jamie's attorney Alex Weingarten said: "Mr Spears did right by his daughter. The conservatorship was for her benefit ... the truth will come out."
Rosengart had previously claimed an attempt to push Britney into a deposition was "retaliatory" and "abusing the legal process".
