The reigning Premier League champions have been working with two-time Golden Boot winner Haaland and Julian Alvarez as their central options for the past two years, but the latter joined Atletico Madrid in a club-record deal earlier this summer.
A lack of starts in the centre-forward role was believed to have been a primary motivation for Alvarez leaving, and City have also sold Liam Delap to newly-promoted Ipswich Town.
As a result, Haaland is currently the only recognised centre-forward in Pep Guardiola's ranks, meaning that Bernardo Silva or Kevin De Bruyne could be shoe-horned into that position should the Norwegian suffer an injury.
Alternatively, City could dip their toe into the transfer market for a backup option in the final few days, and The Athletic claims that Oskarsson is held in high regard by Citizens chiefs.
Man City-linked Oskarsson to leave for £16.9m?
The 19-year-old represented Grotta in his homeland before joining the Copenhagen youth academy in 2020, and he has already made 60 appearances for the senior side, scoring 22 goals and setting up nine more.
Oskarsson had his name up in lights several times during the 2023-24 campaign, where he contributed 15 goals and eight assists from 41 matches, setting up Copenhagen's consolation goal against Man City in their Champions League last-16 second-leg loss.
The teenager has already hit the ground running this term with six goals from 10 appearances in all competitions, and he has two strikes to show from his first eight matches in an Iceland jersey.
Oskarsson is contracted to Copenhagen until the summer of 2028, having only signed an extension a few weeks ago, but the report adds that the Danish side are braced for his departure before the transfer window shuts.
A fee of €20m (£16.9m) will apparently be enough to prise the highly-rated teenager away from Scandinavia, and City are said to be "firm admirers" of the 2004-born attacker.
Will Man City move for Oskarsson before transfer deadline?
However, the reigning Premier League champions are reportedly unlikely to make their move for Oskarsson in the coming days, even though he has been earmarked as an ideal depth option.
Instead, the Iceland international could join Porto - who recently sold Evanilson to Bournemouth - or Real Sociedad, while other unnamed Premier League teams are also in the frame.
While a move for a new attacker has been considered by Etihad chiefs, they will reportedly only push for an eleventh-hour signing if an unmissable opportunity presents itself between now and August 30.
Celtic's Kyogo Furuhashi has also been linked with a late move to the Etihad, but as is the case with Oskarsson, a deal is unlikely to materialise in the coming days.
Haaland's hat-trick helped Man City earn a 4-1 comeback win over Ipswich Town at the weekend, and Guardiola's side return to action away to West Ham United on Saturday.