The announcement prompted a 2 per cent rise in Monument's share price to 47.75p, valuing the business at pounds 418m.
Monument, which is headed by the former Conservative energy minister Tim Eggar, said it had received a number of approaches which may or may not lead to an offer, although no firm proposals had yet been put forward.
The company also repeated the comments it made at the time of its results announcement last month, that it was also looking at ways of pooling its asset base and other technical and financial link-ups with other exploration companies.
This means that the discussions that are being held could result in some form of joint venture rather than a full-blown takeover.
However, analysts said Lasmo was an obvious merger partner for Monument as both companies held stakes in the giant Liverpool Bay gas field. Other partners in the field are Centrica, the trading arm of the old British Gas, and BHP.
Lasmo and Enterprise Oil called off talks on a pounds 3bn merger last week after the two companies agreed that the limited cost savings that could be extracted did not make a deal worth pursuing.
There is also speculation that Enterprise may enter the fray should Lasmo table a bid for Monument.
Monument said last month that it was evaluating merger opportunities in the light of the low oil price and the balance of its own portfolio.
It was being stressed yesterday that the discussions now taking place might lead to Monument making an acquisition.
Apart from Liverpool Bay, it also has interests in Pakistan, Colombia and Azerbaijan, and in Turkmenistan covering the Caspian Sea.
Even though oil prices have recovered from their lows of last year, and are now hovering at just below $15 a barrel, most exploration companies have been forced to cut back on drilling activity and reduce their running costs.Reuse content