The Uruguayan, is one of the hottest properties in Europe and has been in stunning form over the last two seasons in Serie A.
Roberto Mancini is looking to strengthen his attacking options as Edin Dzeko is rumoured to be leaving for Bayern Munich this summer.
According to reports, Italian newspaper II Mattino claims City have already made an offer to Napoli who are keen to open talks with the 25-year-old.
The Manchester side are set to offer Edinson a lucrative five-year deal.
Having scored 49 league goals in 68 league appearances, Cavani has also attracted interest from Juventus who won the Serie A last season.
Although both teams are offering Champions league football next season it is rumoured he is keener for a move to England.