The most likely bidders are thought to be Yorkshire Water, whose territory surrounds York Waterworks and provides the sewerage services for the City, or Anglia Water, which operates in the East Midlands and East Anglia.
However, analysts do not rule out an overseas buyer looking for a secure high dividend income in the UK.
Axa Equity & Law is the main shareholder in York with 26 per cent, followed by Prudential with 13 per cent, Chase Nominees with 8.5 per cent and the directors with 7.7 per cent between them.
The company has an annual turnover of only pounds 9m and 80 employees based in York.
It reported profits of pounds 2.88m in the year to the end of March 1998, down 14 per cent on the previous year, after absorbing the start-up costs of a domestic gas supply business, which was set up 18 months ago in partnership with the shipping operator United Gas.
It already has 20,000 customers countrywide and is expected to move into profit in the coming financial year.
York Waterworks reported earnings of 34.24p a share and paid a net dividend of 13.85p last year.
In the current year analysts are forecasting a profit of pounds 3.75m, earnings of 41.5p a share and a further increase in the dividend to 15p net.
The business is subject to the controls imposed by the water regulator Ian Byatt, but is exempt from the environmental charges paid by regional water companies, which have responsibility for the cost of improving water quality in rivers and on beaches.
The shares had already risen 32.5p on Thursday, in advance of yesterday's jump of 105p.
News of the possible bid excited investors in other small quoted waterworks including Cambridge Water, up 20p to 312.5p, and Dee Valley, 27.5p higher at 480p.