CVC could try to top Imperial Tobacco's £12.3bn ($24.4bn) bid for Gauloises cigarette maker Altadis, reports say.
CVC is the private equity group that abandoned its ambitions to buy the supermarket chain J Sainsbury earlier this week.
The Financial Times reports that CVC plans a joint bid with French private equity group PAI for Altadis, which has rejected Imperial's latest offer.
A spokesperson for CVC declined to comment on the reports.
The newspaper also says Cinven is in talks about joining the bidding consortium.
CVC is linked with Altadis through Carlos Colomer Casellas, who is a member of both the Altadis board and CVC's advisory committee.
Imperial says that its latest offer for Altadis is "full and fair", having raised its initial offer by 4.4%.