Earlier this week ICI rejected an improved 7.8 billion-pound ($15.9 billion), 650 pence-a-share takeover proposal from Dutch chemical group Akzo Nobel.
Dow has asked investment bank Lazard to advise on a possible counterbid, the newspaper said, citing unidentified people familiar with the matter.
None of the parties mentioned could immediately be reached for comment.
By 1109 GMT shares in ICI traded up 0.1 percent at 630p, outperforming the DJ Stoxx European chemical index which traded down 0.1 percent.
ICI, the maker of Dulux paints, has long been tipped as a bid target after slimming down to focus on higher-margin paints and adhesives.
Analysts have said U.S. group DuPont, Germany's BASF and India's Reliance Industries might also contemplate making a bid.
The firm is valued at around 7.4 billion pounds and below Akzo's offer proposal, with some analysts remaining skeptical as to whether the Dutch firm would make an increased offer.
Akzo, which teamed up with German consumer products group Henkel over its proposal, has to decide by August 9 whether it will make a firm bid or walk away.
The Financial Times reported on Wednesday that Akzo was facing a potential rebellion after one of its biggest investors, TPG-Axon, said Akzo's offer for its UK rival, upped to 7.8 billion pounds this week, was too high.
Dinakar Singh, managing partner at TPG-Axon, a U.S. asset manager holding a 3.5 percent stake in Akzo, wrote to the Akzo's chairman to outline his opposition, the paper said.
We do not believe this acquisition is justified by numbers and we fear Akzo's approach has become increasingly desperate rather than thoughtful and disciplined, Singh said in a letter seen by the paper.
A spokesman for Akzo said they had shareholder interests uppermost in their minds.
He declined to comment on the letter and the report Dow was mulling a bid for ICI.
Akzo shares traded down 0.9 percent at 60 euros by 1050 GMT.
ICI will report second-quarter results on Thursday and Reuters Estimates poll shows analysts expect pretax profit of 145 million pounds.