There's been talk from pundits that Cavani is unsettled at United and wants to leave in January.
However, ESPN says the Uruguay international is happy and wants to play out his contract, which runs to the end of the season.
Cavani is waiting for a first start this season but has welcomed the arrival of fellow striker Cristiano Ronaldo.
The 34 year-old plans to hang up the boots after next year's World Cup.
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