The report states that the Red Devils are preparing a shock move to secure the Sweden international with the view to sign him next summer. However, the players £230,000-a-week wages could prove to be a stumbling block.
Ibrahimovic’s contract expires in July meaning he will be free to discuss terms with any club in January.
Galatasaray won the league title for a record 20th time last season and booked a place in the Champions League group stages for the fourth consecutive season.
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.
The 33-year-old striker joined PSG from AC Milan for €30 million back in July 2012.