Regal and Shell both refused to comment on the possible deals. Gazprom and Lukoil, the Russian energy groups, and GDF Suez of France have also been suggested as possible bidders or investors in Regal.
The news emerged as Urals Energy, an Aim-listed company operating in Russia, confirmed that it was "considering different options" for an east Siberian oil field, including a possible joint venture.
Kommersant, the Russian newspaper, had reported that Urals was talking to Shell about selling a stake in the field.
Shell has also been reported as a possible investor in Sibir Energy, a much larger Russia-focused oil group. Shell has also not commented on those reports.
A takeover of Regal would mean a windfall for Frank Timis, founder and former chairman who stepped down in 2005 after disappointing results from the company's exploration activities in Greece.
However, 300p a share is still far below the all-time high above £5 reached in March 2005.
Regal said on Thursday night it had received a number of approaches from companies interested in its Ukrainian gas assets.
It had also agreed to share private information with some of the companies, giving data about its fields.
David Greer, Regal's chief executive, has consistently said it would be better for the company to exploit its reserves itself.
In July it had $174m cash in the bank to pay for its development programme.
Shell agreed last November to pay $410m to take 51 per cent stakes in two of Regal's Ukrainian gas fields, but the deal fell through after Mr Greer, a former Shell executive, was appointed.
Mr Greer said last Friday, when Regal reported interim results, that he had not received a fresh approach from Shell.
The reported approach was said to have been delivered this week, and to have set a deadline of October 20 for talks.
Ukraine, a large consumer of gas without much production, needs to develop a domestic industry. Prices are rising from the deeply discounted levels offered by Russia in the past.
On Thursday Russia and Ukraine agreed to raise the cost of Russian imports to market prices in the next three years.
Regal is taking delivery of two US rigs, contracted for the next five years, to begin developing its assets.
They have since declined, on concerns about Ukraine's legal system after challenges to licences held by Cadogan Petroleum, a London-listed company operating there. Fears of the consequences of escalating tension between Russia and the west have also affected the shares.
Author: Jo Amey
