Jorgensen was the club's No 1 striker target in this month's transfer window.
However, Newcastle's most recent bid, understood to be £15million, was rejected.
The Dutch club had set a deadline for Newcastle to raise their offer for Jorgensen.
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That deadline has now passed, and multiple reports in Holland claim that the 27-year-old will now stay at Feyenoord for the rest of the season.
The news comes in the wake of Daniel Sturridge's decision to join West Bromwich Albion on loan.
Birmingham-born Sturridge chose a move to The Hawthorns over a switch to United for "family reasons".
Newcastle must now look elsewhere for a striker between now and Wednesday night's transfer deadline.