If a bid goes ahead, Dolan could go up against his former boss Sir Martin Sorrell, the WPP chief. The two had a difficult working relationship after WPP took over Y&R in 2000 in a £2.9bn deal.
Dolan stepped down as the chief executive of the agency last year and was succeeded by Ann Fudge, a former president of Kraft Foods.
His resignation from WPP followed speculation that his relationship with Sir Martin had deteriorated. It has been reported that the two had clashed over the future direction of Y&R.
The Wall Street Journal reported that Hellman & Friedman, a former investor in Y&R, is considering linking up with rival private equity firm Kohlberg Kravis Roberts, which has also been reported to be considering entering the race.
KKR is best known for the mammoth £17bn leveraged buyout of RJR Nabisco in the 1980s.
The race for Grey appears to be hotting up, with WPP now considered to be in the strongest position. The hopes of the French group Havas took a knock when its private equity partner Quadrangle was said to be considering withdrawing from the deal.
Quadrangle is concerned over the levels of risk involved in making a bid for Grey, which is thought will attract a price tag in excess of £700m.
Havas suffered more than most during the recession. The group went through a difficult restructure, resulting in more than 1,500 job losses as it slumped into the red.
If Havas did bid for Grey it would not be able to pay in cash, which Ed Meyer, the Grey chairman, is said to prefer. Havas is capitalised at just £800m compared with WPP's £5.6bn.
Another potential Havas partner is the Blackstone Group but it is not thought to be interested in pursuing a bid.
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