The newspaper cited banking sources as saying the indicative offer from Virgin was lower than a recent offer made by International Airlines Group (IAG)
However, Virgin is banking on being able to complete a deal quickly without the regulatory scrutiny that would accompany a merger with IAG, originally formed by the merger of BA and Iberia.
The Times said, without citing a source, that Virgin's bankers are arguing that Lufthansa would be better off doing a quick but lower-priced deal with the airline.
The Virgin offer is thought to be in the region of 50 million pounds, while IAG's is about double that figure, excluding pension and restructuring costs, according to the article.
German owner of bmi is expected to make a final decision on a buyer for its British subsidiary early in the new year, the newspaper said.
The parties involved were unable to be reached for immediate comment.
(Reporting by Stephen Mangan; Editing by Diane Craft)