Hankook is no longer in the running to supply tyres to F1 teams in 2011, but the Korean company is not ruling out another bid within the next "two or three years".
Michelin, Kumho and Avon were also interested in replacing the sport's departing official supplier Bridgestone, but it is believed Pirelli is now in pole position for the deal.
But executive vice president Hyan Bum Cho told the Sydney Morning Herald that Seoul-based Hankook might be interested in succeeding the Italian marque.
"Currently we do have a little Le Mans team, and some rally teams here and there, and we try to sell some motor sports tyres," he is quoted by the Australian newspaper.
"In the future we want to have some hefty market share in that segment. It's quite profitable, but in order to really leverage from motor sports in terms of brands, you need to participate in either world rally championship or a very high segment in Le Mans, or formula one," added Cho.
"So in the future that's the target that we have, to participate in those segments. And that's going to cost a lot of money, a lot of development cost, a lot of investment, and also how to run these operations with experience."
Hankook's Cho confirmed that becoming the new formula one supplier next year was discussed.
"Probably you know that Mr Ecclestone has some trouble with tyres this year. I talked to him personally (but) we decided not to go on with the programme.
"He needed a tyre very, very quick, and we could not prepare it," Cho admitted.
"But we had a very good talk and maybe we'll have a shot for next term, or another term."