By 1147 AEDT, AWE shares were up 14.47 per cent to 83.5 cents each, climbing above the proposed offer price.
The rival bid follows a revised takeover offer on Friday from Chinese state-owned energy giant China Energy Reserve and Chemical Group (CERCG), offering 73 cents per share for AWE.
Oil and gas exploration company AWE (ASX:AWE) announced it received an acquisition proposal from Mineral Resources (ASX:MIN) after the close of trade on Friday, offering $0.80 cents a share.
The offer has been structured as one new Mineral Resources share for each 22.325 AWE shares held.
AWE shares previously had sunk, after the Chinese company withdrew its initial offer of 71 cents a share earlier last week following the target company's refusal to open its books for due diligence.
The mining infrastructure company also said it did not plan to sell any gas from AWE's flagship Waitsia Gas Project offshore as it was committed to supplying domestic gas in Australia, and apprehending increased consumption at its own projects, which are in the pipeline.
With its shares now priced above both takeover offers, it appears as though investors are expecting CERCG to come back with a better offer.