Cable & Wireless (C&W) has confirmed it is in talks with the broadband provider Thus Group and has raised the amount it may be prepared to offer to £330m.
C&W has given itself until 1700 BST to either announce a firm intention to make a firm offer for Thus or to walk away from the deal.
Thus rejected an original approach from C&W, which valued it at around £302m at the end of last month.
C&W has bought 24% of the shares in Glasgow-based Thus.
In a statement to the London Stock Exchange, the two companies said that they had begun discussions about the terms of a potential offer last Thursday, and that C&W had been allowed to see Thus's books.
But the board of Thus said that while C&W's proposal was "worthy of consideration" by shareholders in the absence of a better proposal, it would not be recommending it to investors.
"It is the Thus board's view that the offer is not such a compelling proposal that the Thus board could give a recommendation to Thus shareholders to accept the offer at this time," it said in a statement.
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