Hughton is keen on signing Troisi as winger Elliott Bennett will be out of action for the rest of the year with a knee problem.
The 25-year-old had also been strongly linked with a move to Blackburn Rovers.
Troisi is expected to join Norwich on a season-long loan deal.
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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.