Van Ginkel joined Chelsea in 2013 but has made just four senior appearances for the club, spending spells out on loan at the likes of AC Milan and Stoke City.
Ther 24-year-old has also spent two separate loan spells at PSV, including the second half of last season, and Eindhovens Dagblad reports that the Dutch outfit are now hopeful of making the move permanent.
However, the report goes on to say that no agreement has been reached for the player ahead of his pre-season return to Chelsea on Monday.
Chelsea are still keeping a close eye on Van Ginkel's progress, but he is expected to leave the club again this summer either on loan or on a permanent basis.
The Dutch international signed a new three-year deal with Chelsea in December but is not thought to be in Antonio Conte's immediate plans.