Guilavogui made 19 appearances in the Bundesliga last season as Wolfsburg only avoided relegation through the playoffs, and it appears that he may be allowed to leave the club during the summer.
According to reports in Germany, both the Baggies and the Potters are considering a bid for the 26-year-old, who has earned seven caps for France.
West Brom are in need of reinforcements in the centre of the park after Darren Fletcher was sold to Stoke, but Mark Hughes's side are likely to see Guilavogui as a potential partner for the experienced Scotsman.
Guilavogui may become available due to Wolfsburg signing Ignacio Camacho from Malaga, but any interested club would have to pay well in excess of the £2.7m which Wolfsburg spent last summer.
The former Atletico Madrid man still has two years remaining on his existing contract.