EG Group offered A$3.9 billion ($2.61 billion) in cash for Caltex's convenience store business and separate shares in a new, listed infrastructure and refinery company made up of Caltex's remaining assets, the Australian firm said in a statement without disclosing the offer's total valuation.

EG Group's external spokesman was not available for comment outside office hours.

The offer from the British retailer comes on the heels of a sweetened A$8.8 billion cash bid last week from Couche-Tard, which the Canadian group said was final in the absence of a superior proposal.

Caltex shares were up 0.93% at A$34.82 on Wednesday, still lower than Couche-Tard's A$35.25 per share all-cash offer, indicating investor doubt over the certainty of the deal.

"We think at this stage Couche remains in the box seat but this situation looks to have plenty left in it to run," research analyst Ben Wilson at RBC Capital Markets said in a note to clients.

Morgan Stanley estimated EG Group's offer could be worth anywhere from A$29.32 a share to A$39.77, depending on the multiple assumed for the refining and fuels and infrastructure businesses.

"The EG Group offer would allow shareholders to maintain exposure to the F&I business which has been growing and is a platform for international growth," Morgan Stanley said in a note.

"On the other hand, it also offers exposure to refining which is highly cyclical and difficult to value."

Analysts at Credit Suisse said it was "not clear" whether EG Group's offer was superior to Couche-Tard's, and that an independent expert assessment of the two bids was required given the different structures of the proposals.

Privately owned EG Group entered Australia in 2018 with the acquisition of supermarket operator Woolworths Group's petrol stations for A$1.7 billion.

EG's proposed separate company, dubbed Ampol, would trade on the Australian Stock Exchange and would include Caltex's existing fuel and infrastructure business and international shipping and trading operations.

Under the deal, shareholders will receive about A$15.62 in cash and one share in Ampol for each Caltex share they hold, Caltex said.

The suitor has indicated that it would also consider buying up to 10% of Ampol for an additional cash consideration, Caltex said in a statement.

Earlier this week, Caltex said it would allow Couche-Tard to conduct additional due diligence, after the Canadian firm raised its buyout offer.

Quebec-based Couche-Tard bumped up its cash offer by 2% to A$35.25 a share in a final attempt to sway the oil refiner and convenience store firm, after reports of EG Group's interest in the company emerged.

EG's offer allows Caltex to continue paying dividends before the deal is implemented, and to pay a fully franked special dividend to shareholders to distribute remaining franking credits.

Caltex said its board was considering EG's proposal.

($1 = 1.4954 Australian dollars)

By Paulina Duran and Sonali Paul