The twenty-three year old has attracted interest from Swansea, West Brom, Newcastle, Brighton and Aston Villa according to the Echo.
But manager Jurgen Klopp is not interested in letting the former Tottenham Hotspur player move on from the club.
A £6m bid was turned down for Stewart back in the Summer before the season commenced and Liverpool are now valuing him at the £10m-£12m mark.
Stewart made eighteen appearances for the club during 2016 after making his debut in the FA Cup against Exeter City.
Klopp views Stewart as a good squad player thanks to his willingness and enthusiasm and does not see the point in letting him move on.
The midfielder signed a new five year contract late last year.