The Magpies had a £4million bid for the 20-year-old winger rejected during the recent transfer window.
Ince has impressed for Blackpool in the Championship this season and has already scored four times.
The Mirror reports that Newcastle boss Alan Pardew will make a new attempt at signing the winger in the January transfer window.
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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.