The former Coventry City forward has shone this season, scoring six Premier League goals to fire his side to sixth place in the English top flight.
With only the inconsistent Alvaro Morata and ageing Olivier Giroud to call upon, Chelsea boss Maurizio Sarri is understood to be keen on adding another striker to his ranks, with Wilson a surprise option.
The aforementioned source claims that the 'Blues' have been scouting the 26-year-old with increased frequency in recent weeks and months, with Wilson heavily tipped for a place in the England squad for the upcoming games against the USA and Croatia.
Wilson is currently under contract at the Vitality Stadium until the summer of 2022 having put pen to paper on a new deal back in July.
A fine start to the season has seen Wilson score six times and lay on five assists in 11 Premier League appearances, meaning that he contributes directly to a goal every 88 minutes on average.