The 24-year-old Iceland international scored 24 goals in the Dutch top flight last season.
The Journal reports that Finnbogason was offered to the Magpies during the summer window for a fee of around £5million.
Newcastle decided to look at other targets during the summer.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.