According to The Times, the two buyout firms, which back Karl Lagerfeld and own Formula One racing respectively, are in discussions on forming a consortium to make a bid for the operator.
The news suggests an upcoming battle between private equity firms for O2, which is reportedly set to be courted by KKR, TPG, Bain Capital and Apollo.
Virgin Media owner, Liberty Global, has also said it could make a bid for the company.
Three parent company Hutchison Whampoa was blocked from acquiring O2 by the European Commission over concerns on impact and pricing for UK customers.
O2's parent, Telefonica, had agreed exclusivity deals with Hutchison until the end of June, but is reportedly seeking to end these earlier as a crop of potential buyers circles.