Both have targeted Britain for investments in cash-strapped companies and acquisitions. Anglo United, the loss-making group that owns Coalite and the Falkland Islands Company is another possible target.
Steinhardt has already bought a 30 per cent stake in the preference shares of Ransomes, the lawnmower maker, and has made a recapitalisation proposal, which the company has rejected.
One source said the US companies had been studying LIG and Anglo with a view to buying debt and taking control or participating in a refinancing.
LIG and Anglo have been among the more obvious stock market takeover targets for some time. LIG is planning a refinancing and Anglo is understood to be in need of one.
Michael Steinhardt and Apollo's founder, Leon Black, are among the most colourful Wall Street operators. Mr Steinhardt is renowned for the wild animals kept at his private zoo at Bedford, New York. Mr Black is a survivor of Drexel Burnham Lambert, Michael Milken's collapsed junk bond company. He has since accumulated a fortune that Forbes magazine estimates at dollars 250m.
Steinhardt Partners would not comment on its UK plans. Apollo's representative in this country is the Stellican Group, run by Stephen Julius, a friend of the Princess of Wales. He said Apollo was not involved in any UK deals. However, the Independent on Sunday has established that Apollo has bid for some of Anglo's bank debt.
Stock market rumours have swirled around LIG since it revealed half-year pre-tax losses of pounds 5.1m last December, down from a comparable profit of pounds 15.5m in 1992. At the time James Tyrell, the finance director, said he thought LIG had about six months to turn the business around or lose its independence.
LIG put its photoprocessing subsidiary, ColourCare International, on the market and is shedding 2,000 of 7,000 jobs in its health and personal products division. But it is having trouble selling ColourCare.
James Culverwell, an analyst at the stockbrokers Hoare Govett, said: 'There is an awful lot of buried treasure in LIG in terms of the condom market, the gloves market, and the polyurethane condom which they are launching this month in the US. These are big businesses in these markets and they are world leaders.
'It is a race to see who can find the treasure - the existing management or someone else.'
At the half-year, net debt was pounds 153.9m and shareholders' funds just pounds 109m.
Anglo had negative shareholders' funds of pounds 145m when its balance sheet was last published.
Its broker, Charterhouse Tilney, forecasts a loss of about pounds 45m for the year to March 1994. But before a goodwill write-off of more than pounds 40m it would have lost only about pounds 4m.
There is speculation that its fixed interest rates could be renegotiated as floating rates. In the last financial year that would have reduced the interest charge of pounds 24m by about pounds 6m and resulted in an operating profit of pounds 2m.
Observers say Anglo would be well placed to bid for part of British Coal later this year. But before that could happen it would need to be refinanced, possibly by converting some of its debt into equity.Reuse content