Haaland will be available for around £64.4m (€75m) in the summer of 2022.
There will be plenty of competition for the striker, who scored 41 goals in as many games in his first full season at Dortmund.
Real Madrid and Barcelona are two other clubs from Europe interested in the 20-year-old.
Meanwhile, Cavani ended speculation over his future at United by signing a new one-year deal earlier this month.
But amid rumours of a move for Kane, United manager Solskjaer would not rule out the possibility of signing a striker in the upcoming window.