The initial public offering (IPO) plan comes after a strong period for the group, helped by Star Wars: The Force Awakens and the latest James Bond film, Spectre.
News of the planned float offers further encouragement that the market is recovering from a slow start to the year.
The flotation is expected to value the company at around £1.7bn.
The Sunday Times first reported that accounting firm PwC has been hired to advise on the potential listing.
Vue has declined to comment.
Last month, Vue reported record full-year results after group turnover increased by 17.4 per cent to £180.6m in its last quarter, to 26 November.
Full-year sales totalled £697.9m and the company said admissions rose by 14.4 per cent to 20.6m in the final quarter.
And Vue said the first quarter of 2016 had a "record-breaking start driven by the success of Star Wars Episode VII: The Force Awakens and Deadpool".
The global and UK IPO markets got off to a slow start this year.
But signs of recovery emerged last week, with Dealogic statistics showing growth is expected this month in Europe, the Middle East and Africa (EMEA).
Meanwhile, the biggest IPO in the US market, from BATS Global Markets, completed on Friday.