According to the report, the two clubs have already agreed over a move for the Dutchman, who has two years left on his Blues deal.
The 25-year-old joined the Stamford Bridge side from Vitesse Arnhem in 2013 and has spent campaigns on loan at AC Milan, Stoke City and PSV Eindhoven, where he's been playing since 2016.
Recent reports state PSV are looking to keep the player, who captained them to the Dutch Eredivisie title last season, and are seeking a permanent deal. His Chelsea teammate, Mason Mount, is also a reported target for the side after impressing on loan at Vitesse last term.
The 19-year-old scored 14 times en route to being named Vitesse's Player of the Season and has caught the eye of several scouts. But Frank Lampard's Derby County could also be a destination this summer.
Van Ginkel, meanwhile, was set to rejoin the Blues for their training camp; but given this latest development - if true - that should no longer be on the cards.
The state of affairs at Chelsea is shrouded in uncertainty at the moment, given their managerial dilemma.
Fenerbahce have opened talks with Chelsea over a move for 25-year-old Dutch midfielder Marco van Ginkel. (Talksport)— EPL 365 (@epl_360) June 23, 2018
Antonio Conte remains in charge at the club, but Maurizio Sarri, who has since been replaced by Carlo Ancelotti at Napoli yet is still under contract at the Italian club, is expected to take over the reins at Stamford Bridge at some point this summer.
Players' futures are likely to be affected by any alterations in staff, yet the Blues board have developed a reputation for dealing with transfers without much input from managers.