Grigg is out of contract in the summer and Warriors have opened discussions with the Scotland centre but a report on the RugbyPass claims La Rochelle and Wasps are in the mix for his services.
Grigg could follow Scotland colleagues Stuart Hogg, Finn Russell and Jonny Gray, who is reportedly close to agreeing a move to Exeter Chiefs, out of Scotstoun.
The reports add to the feeling that there will be a big turnaround of players at the end of the season. A number of squad members will be out of contract and some have posted highlights video on social media for potential employers.