The 19 year-old German striker has been linked with several clubs, including Barcelona along with Liverpool, Paris Saint-Germain and Borussia Dortmund.
Adeyemi attended the Golden Boy ceremony in Turin, where he claimed the web-voted prize, with Pedri winning the major award.
"Barca is a great club, it is a source of pride that they love me and of course I can see myself playing there if given the option," Adeyemi told reporters after the Golden Boy ceremony.
"Now they are feeling the departure of Messi but they will always be in the Champions League."
Adeyemi also clarified that he had not spoken to Barcelona president Joan Laporta who attended the function.
However, Adeyemi's agent Thomas Salomon came out after his player's comments, ruling out a Barcelona move in the near future.
"A few days ago we said 'no' definitively to Barca's proposal for Adeyemi," Salomon said according to Sport. "Barca is no longer an option for Karim. The best thing for him is a German club.
"They [Barcelona] made a proposal to us, but they never came to present anything to Salzburg."
Salomon did clarify that Adeyemi could potentially move to Camp Nou at another point in his career, keeping his options open.
"In two or three years we will see what can happen," he said.