With the compensation stalemate dragging on, the teams have asked commissioner Bud Selig to resolve the issue, according to multiple reports Wednesday.
On Thursday, Red Sox general manager Ben Cherington said that he and Epstein have had ongoing dialogue regarding the issue.
"I don't have an update, but I hope there's a resolution, soon," Cherington said.
He would not confirm that the commissioner had become involved but said it's a possibility.
"I can't answer that, other than to say there's been an expectation that at some point the commissioner's office may offer some guidance," Cherington said.
Selig said in October that he thought he would have to become involved to push the teams to terms on Epstein getting out of his general manager's contract in Boston to become president of baseball operations in Chicago.
But the commissioner decided to let the teams resolve the issue themselves. There was talk that the sides would get it done at December's winter meetings in Milwaukee, but that didn't happen.
At the end of December, the teams did agree on one issue: Epstein and the Cubs would be prohibited from hiring Red Sox staff members for three years. That came after the Cubs hired Red Sox area scout Matt Corey and promoted him to national cross-checker.
Epstein has joked that he's not worth very much in compensation. The Red Sox don't agree, reportedly asking for top prospect Brett Jackson or top pitcher Matt Garza at different points of the talks.
The Chicago Sun-Times reported that Red Sox president and CEO Larry Lucchino finally asked Selig to intervene.
Information from ESPNBoston.com's Joe McDonald was used in this report.