The report states that Ibrahimovic claimed that the French Super Cup may be his last game for French giants PSG.
Aftonbladet go onto claim that Galatasaray have held talks with Ibrahimovic and are close to agreeing personal terms.
Manchester United boss Louis van Gaal is also keen on signing the 33-year-old according to the Express newspaper.
Galatasaray are looking to strengthen their squad ahead of this season’s Champions League group stages.
The Lions had a disastrous Champions League campaign under former Italian national team boss Cesare Prandelli last season. The Istanbul giants ended the group stages last with one point from six games and conceded a staggering 19 goals.
Ibrahimovic provided eight assists and scored 30 goals in 37 appearances for PSG last season.
The experienced striker has previously played for AC Milan, Inter Milan, Juventus, Barcelona and Ajax.