Halliwells, LG and Olswang are among an unpre-cedented number of UK firms that are considering flotations or private equity investment once regulations allow.
Almost a third of the firms in The Lawyer's UK 100 now state that they are in favour of allowing the injection of third-party capital.
Speechly Bircham managing partner Michael Lingens said his firm was in favour of law firms being free to attract external investment and that the partners were "considering opportunities".
"In a very crowded mid-market, the issue is, how do you differentiate yourself?" said Lingens. "One route might be an IPO."
LG senior partner Bill Richards said: "We're interested to see if raising external capital would give us the opportunity to improve our business in a way that our current model doesn't give us."
Exclusive research carried out by The Lawyer for its UK 200 Annual Report, which will be published in September, has also revealed that the range of firms in favour of a flotation or injection of external capital is far wider than previously believed.
Olswang managing partner David Stewart said an IPO could be "potentially transformational" for a segment of the legal market, notably as a way for those mid-market firms without significant overseas investment to achieve it rapidly. "Olswang has made no decision on this, but it's certainly something we'd consider," said Stewart.
The world's first law firm to float was Australian personal injury specialist Slater & Gordon, which raised A$35m (£14.58m) on the Australian Stock Exchange on 21 May.
Until now it had been widely thought that it would be volume legal services providers with predictable revenue streams that would be the first to float in the UK.
The list of firms that say they are in favour of external investment, however, includes Charles Russell, Dundas & Wilson, Halliwells, Lovells and McGrigors. The list also includes a number of volume businesses such as Beachcroft, Irwin Mitchell and Keoghs.