The Boston Globe, citing two unnamed sources, reported Epstein will officially leave the Red Sox next week and join the Cubs under a deal that is believed to be worth $15 million.
Epstein will receive what amounts to a $3.5 million signing bonus, the newspaper said.
ESPN cited a "source with knowledge of the talks" as saying the Red Sox would be compensated with minor league prospects, but no major league players would be part of the deal.
The broadcaster said Major League Baseball was concerned over the compensation package, hoping to avoid affecting how other teams compete in the market for front-office personnel.
Ben Cherington, Epstein's top assistant, is expected to be quickly named as his replacement with the Red Sox, the Globe said. His first job will be to hire a replacement for departed manager Terry Francona.