The 31-year-old full-back is said to be looking for an exit from Anderlecht, and with his contract expiring at the end of this season the club are well aware that he will leave for free next summer if no deal can be struck in the coming January transfer window.
The report states that Anderlecht are hoping to convince him to stay, but there is interest in him from Ligue 1, whilst the Hornets have started showing an interest in signing the full-back when the transfer window opens.
A Belgian international, Gillet has played 21 times for his country, whilst registering over 300 appearances with Anderlecht in his long club career - in which he has also played for Gent, Eupen and French side Bastia.
Do Watford need Gillet?
Allan Nyom is undoubted first-choice right-back at Vicarage Road, but there is a worrying lack of cover should he get injured, or lose form as appears to have been the case in recent weeks.
Juan Carlos Paredes can fill in, but he is not a solid choice defensively, whilst Ikechi Anya can also play there, but it is his weakest position.
Gillet would be a solid and reliable option to bring in, if he could be convinced to simply play a covering role to Nyom. There are no guarantees for first-team football, and the 31-year-old surely wants to be playing every week at this current stage of his career.