Shares of Cubic at last check were 1.7% higher at $76.06.
In February, Cubic agreed to be bought by private-equity firm Veritas Capital and hedge fund Elliott Management. The companies agreed to pay $70 a share to take Cubic private.
Last week, however, Cubic unveiled an unsolicited proposal from Singapore Technologies Engineering STE for $76 a share, or roughly $2.4 billion, cash.
Elliott Management declined to comment. Cubic and Singapore Technologies did not immediately respond to a request for comment.
Singapore Technologies said it intended Cubic to be the global headquarters of its smart mobility business.
At the time Cubic said its board had "determined to engage in discussions with STE to further evaluate the merits and risks of the proposed transaction.”
Since then, the private-equity duo raised its bid to $72 a share, and Singapore Technologies responded by boosting its offer to $78, The Wall Street Journal reports, citing people familiar with the matter.
In September, Cubic said it had adopted a poison pill in response to a takeover approach by Elliott Management.
A poison pill, also known as a shareholder-rights plan, is designed to make a hostile takeover prohibitively expensive.
Last week, Cubic said Nuvotronics, which operates within its Cubic Mission & Performance Solutions division, won a contract valued at more than $10 million from the Defense Department.
The contract is to develop a dual-band, ultra-high performance and low size, weight and power 5G wireless network communications transceiver for military applications.