Honda has supplied engines to BAR for four years and is keen to increase their involvement in F1.
The BBC reports that it has agreed to buy a minority stake in the team for a substantial sum and started a management shake-up.
BAR's parent company British American Tobacco (BAT) will now form a joint venture company with Honda which will replace the existing structure, with BAT retaining a controlling 55 per cent stake.
Richards - who successfully blocked star driver Jenson Button's attempt to move to rivals Williams earlier this year - has been ousted a year before the end of his contract as a result of the reshuffle, but he remains positive.
"We were brought in by British American Tobacco to turn the team around and secure its long-term future and that is what we have done," said Richards, whose Prodrive organisation also challenges for international titles in rallying and sportscars.
Richards, 52, will stay in a consultancy role until the end of February.
