British business magnate Bernie Ecclestone said he would sell his 5.3% stake in F1 when CVC Capital Partners exits the business.
Private equity firm CVC is the controlling shareholder of the F1 with a 35% stake.
"If I sell I would sell with CVC. If somebody wants to buy CVC's shares but doesn't need mine then I will keep them," the Daily Telegraph quoted Ecclestone as saying.
Ecclestone is due to undergo a trial in Germany over allegations that he paid bribe to steer the sale of F1 to CVC in 2006. The bribery allegations had stopped CVC's plans for an IPO in Hong Kong in 2012.
German media company Constantin Medien AG accused Ecclestone of bribing a German banker, to ensure F1 was sold to CVC at a lower valuation.
Ecclestone denied the charges and has stepped down from the board of F1's parent company Delta Topco until the trial comes to a close in September. In February, he won in a UK lawsuit stemming from the allegations.
The estate of collapsed investment bank Lehman Brothers, the third largest shareholder in F1, is also looking to sell its 12.3% stake by 30 June to pay its creditors.
"Lehman had the opportunity to sell lots of times," Ecclestone said.
"Lots of people tried to buy those shares and they won't sell. Maybe they would sell at an over-rated price. The obvious thing is for them to sell along with CVC too."
Meanwhile, CVC wants to retain its stake in F1 as long as its value is accelerating, the newspaper reported citing a source close to the company.
Having generated a return on investment of more than 350% from the business, F1 is one of CVC's most profitable assets. It bought F1 controlling stake for $2bn (£1.2bn, €1.4bn) that was partly funded with $1.1bn debt from the Royal Bank of Scotland.
CVC has right of first refusal if any of F1's minority shareholders want to sell.