Chevron Texaco is in talks to take a 25% stake in Yukos, the Russian oil giant at the centre of an official probe, the Sunday Times reports.
Mr Khodorkovsky denies all charges
The US oil giant has been courting Yukos for some time and is understood to have made a $4bn offer, the paper reports.
It said the offer had been triggered by the possibility that Yukos' planned merger with rival Sibneft might be in difficulty.
A series of investigations into Yukos by the Russian authorities has raised doubts about the Sibneft tie-up, but both companies have said it is on track for completion.
Yukos CEO Mikhail Khodorkovsky has been targeted by prosecutors in what is being seen as a campaign by Kremlin figures to keep business people out of politics.
The investigation began in July, with the arrest of one of Yukos' key shareholders, Platon Lebedev, who was charged with tax evasion and theft of state property.
That was followed by a search of Yukos' archives and a criminal investigation into several murder and attempted murder cases of officials and businessmen who had conflicts with Yukos.
The company has denied all charges.
Mr Khodorkovsky said at the weekend the investigations were politically motivated - and far from over.
"These cases have absolutely nothing in common with reality and come from political orders," he told the Associated Press.
Russian President Vladimir Putin has avoided commenting directly on the affair but officials have said he is concerned about the effect it is having on the economy.
Both Mr Putin and Prime Minister Mikhail Kasyanov have described the detention of businessmen suspected of economic crimes as excessive.
But government sources say Mr Putin cannot rein in prosecutors which are independent of the government.
The Russian stock market has fallen by about 8% in the past month.
And there is concern capital is starting to flow out of the country as a result of the investigations.
Meanwhile, the Interfax news agency said Russian investigators have launched another probe into a subsidiary of Yukos.
The latest enquiry is said to centre on the sale of 19.85% of the shares of a company called Yeniniseineftegaz to Maastrade Ltd, a Cypriot-registered subsidiary of Yukos.
It brings the total number of investigations into Yukos or its subsidiaries to eight.
Last week, ChevronTexaco said it had increased its quarterly profits four times to $1.6bn on the back of higher oil prices.