Citgo Petroleum has reportedly received revised offers from at least four bidders this month, some of which have valued Venezuela's American oil refining unit at over $10bn.
Firms that tabled bids include Marathon Petroleum, Valero Energy, HollyFrontier and a private equity consortium of TPG Capital and Riverstone Holdings, Reuters reported.
Some bids valued the firm at more than $10bn (£6.3bn, €8bn) while others valued it below $7bn.
However, it is still unclear if Citgo's owner will press ahead with a sale of its US refining and marketing unit as Venezuela's finance minister Rodolfo Marco has said that Citgo's assets will not be disposed.
Bidders held different views on the fluctuating value of crude oil held at Citgo's refineries, future oil purchases from Opec member Venezuela and potential environmental liabilities.
Lazard, the investment bank roped in by Venezuelan national oil firm Petroleos de Venezuela SA (PDVSA) to explore a sale of Citgo, has not told the bidders if there will be an additional round of bids, the report said.
A first round of bids this fall attracted several other contenders, including India's Reliance Industries and PBF Energy. Those parties are no longer in the fray, it added.
Pursued by Reuters, Citgo refused to comment.
Lazard, PDVSA, Marathon and HollyFrontier did not return requests for comment.
TPG, Valero and Riverstone also refused to comment.
Citgo pays out huge dividends to PDVSA. Lower oil prices are adding to Caracas' debt woes because they hit the revenue it rakes in from oil production, making it more open to raising cash through a sale of Citgo.
Capital Economics said in a 28 November note: "The writing is on the wall for Venezuela as falling oil prices exacerbate severe strains in the balance of payments. Both the government's ability and willingness to service its foreign currency debt will be tested over the coming months, and we continue to think that a default is more likely than not in the next two years. As a result, foreign currency bond yields look set to remain very high."
Earlier in November, energy major ConocoPhillips said in a US court filing that the Venezuelan government was using the sale of Citgo to hamper Conoco's ability to collect an expected arbitration award after its Venezuelan oil assets were nationalised in 2007.
In a 26 October interview, published in the El Universal newspaper, Marco said Citgo's sale "has been ruled out."