ICI has agreed to open its books to suitor Akzo Nobel after the Dutch chemicals group sweetened its indicative offer for the UK firm.
The Dulux dog is a famous image in the world of UK advertising
The 670p a share offer, which values ICI at about £8bn ($16.3bn), comes days after the Dulux-maker snubbed Akzo's £7.8bn approach.
ICI had said that the earlier offer had undervalued the firm.
But the deal may still face opposition from competition watchdogs, rival bidders or Akzo investors.
"The Board of ICI has agreed that Akzo can undertake certain limited due diligence, which ICI expects to be completed within a few days," ICI said.
But the company added that there was no certainty that the approach by Akzo would lead to an offer being made.
Last month, Akzo made its first approach to ICI with a 600p a share offer, which it later raised to 650p.
Its latest approach of 670p a share represents a 41% premium on ICI's share price when it made its first offer.
But even if Akzo does make a firm offer for ICI, its bid faces a number of hurdles, including being gazumped by rival bids from the likes of US firms Dow Chemicals or DuPont, Germany's BASF or even India's Reliance Industries.
Analysts have also suggested that a takeover could attract the attention of competition watchdogs, as Dulux has 40% of the UK paint market while Akzo's Crown Paints has 14%.
In addition, Akzo shareholders, particularly hedge funds, who own an estimated 25% of Akzo stock, have voiced fears that the latest offer is too high a price to pay.
TPG-Axon, a £5.3bn fund which holds a 3.5% stake in Akzo has already written to the firm stating its opposition to the ICI deal.
Akzo has had plenty of cash to spend on an acquisition after selling its pharmaceuticals business Organon BioSciences to Schering-Plough for £7.4bn.
It has also struck a deal to sell ICI's adhesives and electronic materials businesses to its German rival, Henkel, if the takeover goes ahead.