Chase Carey says his negotiations with the teams over the next Concorde Agreement are "on the right track".
The current commercial agreements expire at the end of this year, and Liberty Media has made no secret the new deal should memorialise significant changes in the way income is distributed and rules are made.
"It's on the right track," France's Auto Hebdo quotes Formula 1's CEO as saying.
"After the ratification of the new regulations for 2021, we are at an advanced stage with the teams concerning the new Concorde Agreements which will strengthen their economic model and promote the growth of the sport."
Carey does at least appear to have succeeded in mainly keeping the negotiations - which are historically politically fraught - out of the headlines.
"It's better to wait until it is signed before saying more, but we feel that we are achieving the goals we set for ourselves to make the sport healthier," he said.
"These new agreements represent significant progress in terms of costs, revenues, redistribution and the like."