Under terms of CYBG's revised proposal, Virgin Money shareholders would own about 38 percent of the combined group as compared to the original 36.5 percent offer.

The proposed combination would provide a full-service banking offer for around six million personal and business customers, CYBG, the owner of Clydesdale Bank and Yorkshire Bank, said in a statement.

The reported new offer comes after CYBG made an all-share takeover proposal last month that at the time valued Virgin at about 1.6 billion pounds.

As things currently stand, CYBG has until 1700 GMT on 18 June to make a firm offer or walk away from Virgin, under rules set down by Britain's Takeover Panel. The deadline could be extended further with the consent of the takeover panel, at Virgin Money's request.

Since the original offer, Virgin, which was founded and is partly owned by entrepreneur Richard Branson, has been tight-lipped about the bid, saying only that it was reviewing the proposal.

Sky News reported the revised bid earlier on Sunday.

(Reporting by William James. Editing by Jane Merriman/David Evans)