The Manchester United playmaker is seeking regular playing time after finding himself on the periphery at Old Trafford.
The Red Devils have yet to decide if they will let Lingard leave this month.
Sky Sports says an official approach from Nice will arrive next week.
Lingard, 27, played in the FA Cup win over Watford last weekend, but has not featured in the Premier League in over a year.
A graduate of United's academy, Lingard is under contract until 2022.