The teenager has started the new season in sparkling form, scoring 18 goals in 11 appearances for the Austrian side.
That included a first-half hat-trick on his Champions League debut against Genk in September, which made him the third-youngest player to score a treble in the competition after Raul and Wayne Rooney.
According to the Sun, Manchester City are interested in bringing the striker to the club his father Alf-Inge used to play for between 2000 and 2003.
However, they will face competition from cross-town rivals United, as well as El Clasico giants Real and Barca.
The Premier League champions sent scouts to watch the player in action against Liverpool in the Champions League at the start of October.
Haaland found the net in that game as the Austrians incredible fought back from three goals down to level the scores, only for the European champions to find a winner through Mohamed Salah.
A source at Man City told the newspaper: “We had scouts at Anfield to watch him in action. They were very impressed with what they saw.
“We feel we would stand a good chance of getting him if we put something on the table to his club.
“We like his age and his link-up play. He would have watched the club a lot as a very young boy.
“His dad was a big favourite with the fans and there is a hope that will continue with his son one day.”
Salzburg hope to bring in £50 million with Haaland’s sale but a January deal is unlikely as the Austrians would prefer to do business in the summer.
Haaland, who has a contract with his current employers until 2023, has been talked about as a long-term successor to Sergio Aguero.
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