Wilson is in incredible form in the Premier League this season, scoring six and helping another 7 to help Cherersh until the sixth place in the table.
That return saw his first retreat from England for the current international break and he correctly achieved his debut in a friendly victory over the United States last week.
The 26-year-old player had a remarkable increase in recent months after two serious injuries to his knee almost ended his career.
And now it can be set to leave the South Coast in the near future with a circle of top clubs.
Bookmakers Coral made Chelsea favorites 2-1 the next Wilson club.
Liverpool and Tottenham are the closest rivals to the blues of the betting markets, but are somewhat behind.
Harry Eitkenhead for Coral told Starsport: "If Kalum Wilson continues the career of his current trajectory, then his future may lie further from Bournemouth.
"We made Chelsea the most likely next destination for the highly-rated striker and a move could come this summer."
Wilson enjoyed the unforgettable evening last Thursday when he started in England against the United States.
Despite missing a few good chances, Bournemouth striker led to a 3-0 victory in the opening to open his international account.
He said: "I have no words, at the moment it's not hotter.
"It was an opportunity for me and I just wanted to grab it with both hands." Wayne Rooney is a legend for England to receive my shirt from him before he is a great honor and share the pitch with him.
"His chapter is now over and my start begins. I thought that the chance left, I knew that time is not on my side, I saw Marcus Rashford standing and I think I had a few minutes.
"It's a day I will appreciate for the rest of my life."
Wilson will hopefully keep his good result in appearances when Bournemouth will host Arsenal in the Premiership on Sunday.