Boehly and co-owner Behdad Eghbali, of ClearLake Capital, are said to have fallen out over the running of the club.
Both ESPN and Sky Sports state that ClearLake Capital will not sell - and that their full focus will be on creating long-term stability in the London club.
ClearLake Capital owns 61.54% of Chelsea. The remainder is shared between Todd Boehly, Mark Walter and Hansjörg Wyss.
According to ESPN, the relationship between Boehly and Eghbali has deteriorated.
No direct talks between any individual investor and ClearLake Capital are said to have taken place.
At the same time, ClearLake Capital would consider buying a larger share of the club.
Sky Sports also says Boehly would be open to selling his share, after just over two years at the club.