Bild also report that Borussia Dortmund are leading thechase for the 19-year-old but Manchester United also hold an interest in the striker.
During his time at Molde current United Coach Ole Gunner Solskjaer did work with Haaland.
Solksjaer did leave Molde for Salzburg in January of 2019.
But they are just two of a number of clubs who are monitoring the striker.
Last month, Norwegian newoutlet G said that there were 11 major European teams scouting him.
As well as Dortmund and United, it was claimed that Barcelona, Real Madrid, Bayern Munich, Juventus, Manchester City, Chelsea, Arsenal, Valencia and Sevilla were all monitoring Haaland's progress.
Haaland has scored eight goals in the Champions League so far this season, including a hat-trick in his side's 6-2 win over Genk.
Haaland, a Norway international, has the chance to dump Champions League holders Liverpool out of Europe's elite club competition next week when they host Jurgen Klopp's men in a decisive Group E match.
'They are the world's best team,' Haaland said of the match.
'But we know we are good at home and if we are at our top level, we have a chance.'
He is the son of former Leeds and Manchester City midfield player Alf-Inge Haaland and was born in England, growing up a Leeds supporter.
