The Dutch outfit are looking to bring in some new faces for their midfield positions as Georginio Wijnaldum is still out with an injury till the end of February and Ola Toivonen is likely to leave in the upcoming transfer period.
Hazard, the 20-year-old younger brother of Eden who joined the Blues soon after his sibling in 2012 from Lens, is currently in his second loan spell with Belgian club Zulte Waregem.
He is playing well, having done enough to break into the national squad, and he impressed PSV when the two teams met in the third qualifying round of this season's UEFA Champions League.
The Dutch side have since followed his progress intensively but have now admitted defeat in their attempts to lure him to the Eredivisie.
PSV technical manager Marcel Brands told Dutch football website Voetbal International: "He wants to stay in Belgium. So is he not attainable."
According to reports in the Belgian media, Hazard has already agreed on personal terms with Anderlecht about a loan deal till the end of the season, although Waregem have not given up in their desire to keep him.