The Magpies have had an initial bid for the 27-year-old Denmark international rejected with the Eredivisie club understood to be holding out for a fee in the region of 20million.
However, reports claim Newcastle are still in the hunt and, with owner Mike Ashley having sanctioned a recruitment drive during what remains of the winter transfer window, they could yet break their transfer record to land Jorgensen.
That currently stands at the £16million they paid Real Madrid for England striker Michael Owen in August 2005, long before Ashley took up the reins at St James' Park.
Jorgensen, whose former clubs include Brondby, Bayer Leverkusen and Kaiserslautern, joined Feyenoord from FC Copenhagen in July 2016.
He has scored seven goals in 14 league appearances to date this season and two more in his four Champions League outings. However, Robin van Persie's return to his former club earlier this week has increased competition for places and the Magpies are hoping to persuade the frontman that his future lies on Tyneside.
Jorgensen is not Benitez's only target with Leicester's Islam Slimani also understood to be on his radar.