The transfer window shuts by 5pm, and the Toffees are most likely putting plans in place to go after the 21-year-old once they fail in their attempt to land the Ivorian.
Everton director of football Marcel Brands is a big fan of Bergwijn, who scored 14 in 33 Eredivisie games last term, and he knows him well from his days at PSV.
The Blues chief would use his connections at his former club to try and set up a late move for the Dutch international, and that will help soften the potential blow of missing out on Zaha.
West Ham United and Tottenham have also once registered in the speedster, and he even caught the attention of Spanish giants Barcelona as a result of his huge potential and ability to rip defences apart with his direct style of play.
Bergwijn has three years left on his current PSV deal, but the club could be willing to do business if the right amount is offered.
Everton need such a quality attacker in order to boost their chances of finishing in top-seven this season, and at his age, he will only get better and can be a long-term option.
The Netherlands international fits the club’s new policy of buying young players, and he definitely brings quality to the table.