Haaland, 21, has a £63million release clause which becomes active in July - and a host of Europe's top clubs are already racing for the striker's signature.
According to the Daily Mail, the Norwegian is expected to snub interest from Real Madrid and choose Premier League champions Man City.
The report claims personal terms have already been discussed and the framework of the deal is agreed.
City have thrived without a recognised centre-forward this season, establishing a six-point lead at the top of the table, but the gap in their squad up front remains prevalent.
Madrid, meanwhile, are expected to secure a deal for Paris Saint-Germain star Kylian Mbappe.
Spanish outlet Marca report that PSG have given up hope of agreeing a new contract with the France star, who is expected to sign pre-contract terms with Madrid as early as next week, ahead of a free transfer which will be announced in the summer.
However, ex-Republic of Ireland striker Tony Cascarino believes Mbappe would be best-suited at the Etihad, describing the 23-year-old as a better fit than Haaland and former City target Harry Kane.
"All three are great players," the Weekend Sports Breakfast host said on talkSPORT. "They would benefit any club in the world.
"Harry Kane, Erling Haaland, Kylian Mbappe - if you gave me those three, which one of them would suit Man City best? I would say Mbappe.
"His versatility as a player and his explosive speed would be the difference in giving City something they don't have.
"They've got so many players who make assists and I think his goal record would get even richer.
"I think he would fit City better than anybody in the world of football."
And ex-City defender Micah Richards also believes Mbappe ought to snub the Bernabeu to join a Premier League club.
Following PSG's Champions League exit at the hands of Madrid, Richards told CBS Sports: "I don't think he should go to Real Madrid. His mind might be already made up.
"But I would be going to Manchester City or Liverpool. They are the two best teams consistently, I would say in Europe.
"Yes, people will say 'Man City have never won the Champions League'. But, the way they play, the points record. I would be going to either Liverpool or Man City."