The company, which serves residents and businesses in its region, has appointed Robert Fleming its banker to advise on a sale, which could take place as early as this autumn.
Other flotations by UK phone companies have included Colt Telecom Group, which is emerging as the top-performing stock in London this year, and Energis, whose shares have more than doubled in value.
Kingston is not expected to be as successful as Colt and Energis, which own fibre-optic networks that cream off lucrative corporate accounts, but it has a strong regional presence.
"Our directors and shareholders and Hull City Council are in discussions about refinancing the business and those discussions are ongoing," said a spokesman for Kingston. "But there's no timetable and no prospectus."
New management took over at Kingston last autumn. Steve Maine, a former BT executive, joined as chief executive and Ross Cope, a former executive at Bell Cablemedia - a cable company bought by Cable & Wireless - as finance director.
Kingston has a monopoly in the region it serves around Hull. The company was the only one licensed to serve the area until 1991, when telecoms were opened to competition. Since then, no company has decided to compete. The telecoms regulator is carrying out a review of Kingston's licence, which it expects to conclude in July.
Kingston bought control of Yorkshire Electricity's telecoms arm, Torch Telecom, in 1996. Torch owns a broadband fibre-optic network that sells high-margin services to corporate customers in Yorkshire. Kingston also owns: KTL, a telecoms equipment testing lab with sites in the UK, the US, Canada and the Netherlands; an internet service provider, Kingston Internet; and Kingston SCL, a software company.
Unlike phone companies with big fibre-optic networks, the sales of other telecom stocks such as Ionica and Telewest, have disappointed shareholders. Fibre-optic networks can undercut local phone companies as their technology is more efficient.
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