UK watchdogs have set a deadline of 30 January for Tata Steel and rival bidder CSN to table further offers for Anglo-Dutch steelmaker Corus.
A merger would create the world's fifth largest steel producer
The Takeover Panel warned that it would begin an auction procedure if the two remained in competition.
Both companies had agreed to the decision, the panel added.
Brazil's CSN tabled a £4.9bn ($9.6bn) offer for Corus last week, trumping a revised £4.7bn offer made by Indian steelmaker Tata.
The new 515 pence-a-share bid from Companhia Siderurgica Nacional was accepted by Corus on 11 December, beating Tata Steel's offer of 500p a share.
A takeover of Corus by either firm would create the world's fifth-largest steel group, producing 24 million tonnes of steel each year.
The Takeover Panel added that either company could revise its bid up until the close of trade on 30 January.
The battle for Corus comes amid growing consolidation in the global steel industry.
With prices and demand soaring, Mittal Steel - the world's largest steel firm - bought European rival Arcelor for $34bn earlier this year.