The 38-year-old recently confirmed that he had left Los Angeles Galaxy following two campaigns during which he scored 52 goals in 56 MLS games.
Having enjoyed spells at Juventus, Inter Milan and AC Milan previously in his career, Ibrahimovic has been tipped to make a return to Serie A.
According to The Sun, AC Milan and Bologna are leading the race to secure the Swede's signature.
It is claimed that Ibrahimovic will demand a contract worth almost £215,000 a week.
While Milan would represent a familiar climate for Ibrahimovic, moving to Bologna would see the striker reunite with manager and old friend Sinisa Mihajlovic, with whom he worked briefly at Inter in 2007 and 2008. body check tags ::