The possible mega-swap has been rumoured on a number of Twitter sources and it has been suggested that Dzeko plus some cash could tempt Arsenal into selling.
Arsene Wenger has made it clear that if van Persie is to leave Arsenal, that it should be early in the summer to avoid a repeat of last season.
Arsenal started the season with Cesc Fabregas and Samir Nasri still among their ranks, despite both players openly admitting to wanting to leave the club months before the season started.
The Dutch striker has confirmed that he won't be signing a new deal at the Emirates and he could be open to a move to Manchester City in order to win more trophies.
Van Persie finished the 2011/12 season as Premier League top goalscorer and winner of the PFA Player of the Year award.
Last season's Premier League winners are in the market for new forwards and both Dzeko and Tevez have been linked with moves away from the Etihad.
The possible swap has been backed by Arsenal legend Ray Parlour who earlier said:
"I don’t know what Arsenal will look at, but if RvP does want to go to City then they could look at a swap deal with Dzeko."
The Bosnian arrived at Manchester City in January 2011 from VfL Wolfsburg for a reported £27million.
Despite scoring 16 league goals in 45 appearances, including a vital 92nd minute equaliser in the 3-2 win over QPR that secured the title for City, the club are willing to take a loss and sell him this summer.