Macmahon has already struck a $29.6 million deal with Leighton Holdings over the sale of its construction business, rebuffing previous offers by Sembawang.
Macmahon said today that it had received another offer from Sembawang which valued the construction business at $5.4 million more than Leighton's offer.
"The board is considering the proposal and will continue to keep the market informed in accordance with all legal and regulatory requirements," Macmahon said in a statement.
In a letter to Macmahon, Sembawang said it was prepared to make an unconditional offer, subject only to the execution of a formal sale and purchase agreement with Macmahon.
"Our offer addresses all of the Macmahon board's earlier concerns and clearly is in the interest of Macmahon's minority shareholders," Sembawang Engineers and Constructors chief executive Richard Grosvenor said.
"We consider our unconditional offer to be superior to Leighton's proposal."
At close of trade today Macmahon's stock was up nearly 3 per cent, trading at 34.5 cents.