The mystery bidder has offered to buy Cole and its optical interests for $321m, or $19.65 per share. News of the offer resulted in shares in the group soaring as much as 70 per cent.
Speculation as to the identity of the bidder this week was rife, with many suggesting Luxottica, after its shares also rose.
While the official stance is 'no comment', Cole is certainly a lucrative prospect for the Italian group Ð it owns 6.5 per cent of the $16bn US optical market, and revenue for the first six months of this year was $600m.
If it were to acquire the company, Luxottica would run the two largest optical retailers in the US, as it already owns market leader LensCrafters.
Cole has more than 2,000 outlets through a number of brands, including the Pearle Vision chain of more than 800 practices. It also owns 21 per cent of Pearle Vision Europe, one of the largest retailers on the Continent with 1,400 outlets and annual sales of $700m.
The majority shareholder of Pearle on the continent is Hal Holdings, a Dutch private equity company, which has a stake in Vision Express' French parent company GrandVision.
Following PAI Investments' E491m takeover bid last month, Hal stopped just short of the threshold that would force it to launch a buy-out bid for GrandVision, but is now the largest single shareholder. Hal owns a 20 per cent stake in Cole.
Cole announced last week that director of the company, Melchert Groot, had resigned citing 'conflicts of interest'.
Groot is also chief executive of Pearle Europe and is on the board of Hal.