SmartSpace Software PLC said it is considering the 82-pence-per-share offer from Australia's Skedda Holdings Inc and is consulting with advisers and major shareholders.
The provider of space management software noted that it had rejected a previous bid at a lower price and that the subsequent possible cash offer was unsolicited and conditional.
It urged shareholders to take no action at this time and noted that there is no certainty either that an offer will be made.
Under London's put-up-or-shut-up rules, Skedda must make a firm offer by 5pm on 9 January or announce that it does not intend to make an offer.
Shares in SmartSpace were up another 3% to 73.70p, having more than doubled from 34p yesterday.