The report claims Ibrahimovic is being lined up as a potential alternative to Napoli striker Edinson Cavani. Should a move for Cavani - who remains first-choice - fall through, then City will push ahead for Ibrahimovic.
City director of football Txiki Begiristain has had talks with Ibrahimovic's agent, Mino Raiola. The 'super-agent' recently admitted Ibrahimovic is not guaranteed to be at Paris St Germain next season.
The Swedish striker joined the club from AC Milan last summer, and is currently top scorer in Ligue 1 while PSG sit top of the table.
Juventus and AC Milan are also tracking Ibrahimovic, but Roberto Mancini's ties with the striker - he coached him at Inter Milan - could help City.
Begiristain and Raiola are also thought to be close, and Begiristain was the man behind the Ibrahimovic to Barcelona transfer back in 2009.
But much depends on the success of City's pursuit of Cavani. The Uruguayan international has been tracked by PSG, and the French club may look to draft in Cavani if they lose Ibrahimovic.
The Swedish striker's £11.5m-a-year salary could put off some clubs, but City are one of the few in the world with the financial muscle to sign the 31-year-old.
The report claims Napoli have not received any formal offers for Cavani at the moment, but City are ready to spend big this summer in an effort to regain the Premier League title.