Enzo Maresca shipped Jackson out to Bayern Munich on loan last summer after their relationship broke down, and the Senegalese striker scored 11 goals in 34 appearances for the club.
The 24-year-old is set to return from his loan in Germany after his World Cup campaign, and then, Xabi Alonso will decide on his immediate future.
Jackson is one of four strikers currently on Alonso's books in West London, joining the likes of Joao Pedro, Liam Delap and Emmanuel Emegha.
Whilst that is expected to be too many, Jackson "would be willing to stay at Chelsea" - according to the Daily Mail - with the forward keen for his fair amount of game time.
Any final decision on Jackson and their other striker options will be made between Alonso and Chelsea’s sporting leadership team.