(Reuters) -One Rock Capital Partners, a U.S. private equity firm, is one of the few remaining bidders for BP's Castrol lubricants business, Bloomberg News reported on Wednesday, citing people familiar with the matter.

One Rock declined to comment, while BP did not immediately respond to a Reuters' request for comment outside regular business hours.

The private equity firm is bidding for the entire asset, the report said, adding that Canada Pension Plan Investment Board, another interested party, is only interested in taking a minority stake.

Deliberations are ongoing. One Rock and CPPIB could decide against proceeding with their offers, as per the report.

Reuters reported in May that BP kicked off the sale of the Castrol lubricants business, which could raise between $8 billion and $10 billion. Saudi Aramco was one of the parties considering a potential bid for the business.

Bloomberg previously reported that the lubricants business also attracted interest from companies such as India's Reliance Industries, buyout firms Apollo Global Management and Lone Star Funds, among others.

Several big-name energy companies and financial suitors have dropped out of the bid and valuation expectations have slipped, Bloomberg reported on Wednesday, adding that BP may also opt to keep the asset for longer.