Trinity Mirror has said the paper is not for sale, but newspaper reports claim that an improved bid could be accepted because Trinity does not see it as a core asset.
Cook, Labour MP for Livingston, is a keen punter and supplements his political income by writing a monthly column in the title.
It is part of Trinity Mirror's sporting publishing division and sells around 76,000 copies a day. It is reported to have made an operating profit of around £17.5m last year.
Cook said: "The Racing Post is my favourite newspaper. I am happy to help out the owners in whatever way I can now and in the future. I want the paper to survive, whether it's with Trinity Mirror or not."
The title is the latest media property to attract the interest of the private equity sector, which has a lot of spare cash and is searching for investment opportunities.
ITV, The Wireless Group, Virgin Radio and Trinity Mirror itself have all been recent subjects of private equity interest.
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