Kennedy joined Mjällby from GIF Sundsvall in November and has been a regular in Sweden's Under-16 national team, scoring four goals in 12 appearances.
He featured for Mjällby's senior side in pre-season, scoring in a friendly against Artis Brno. He is contracted to the Swedish champions until 2028.
One unnamed Italian club and Wolverhampton Wanderers — currently relegated from the Premier League — are understood to have made the most concrete approaches so far, with first contact established with Kennedy's camp, reports Fotbolltransfers.com.
His agent Georgios Kousis said: "It's incredibly exciting to see such significant interest, but it's not unexpected. 'Zebbe' has incredible potential and has delivered when given the chance.
"He's in a fantastic environment right now, so we are not in a hurry. But it's absolutely flattering and we are in close dialogue with the clubs following him."