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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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