Now recuperating from a serious knee injury, there has also been talk that Manchester United could offer him a new deal if he can recover in time for January.
But Galaxy are about to face stiff competition from new MLS outfit Los Angeles FC who are looking to sign a marquee name to start off their time in the league next year.
Having left Manchester United last month, rumours have been rife linking Ibrahimovic with a move across the Atlantic, with LA Galaxy at the head of the queue for the striker.
According to multiple reports out of England, the Galaxy and Ibrahimovic have discussed a deal that would make the 35-year-old the highest-paid player in MLS history at $7.7 million per season.
The Los Angeles Galaxy are struggling to sell tickets for their pre-season friendly against Manchester United. However, Galaxy's rumoured interest has seemingly put the breaks on any deal - but head coach Curt Onalfo has refused to substantiate the speculation. MLS clubs are allowed a maximum of three players whose wages exceed the club's salary cap, but those positions are now occupied by Romain Alessandrini, Giovani dos Santos and Jelle van Damme. Romelu Lukaku has been brought in from Everton to help fill the void.
The five-time MLS Cup winners may be forced to downgrade Ibrahimovic's basic wage to ensure he can be added to their squad during the second transfer window of the year, which runs from 10 July-9 August.