Rooney ended last season as the second highest scorer in the Premier League but went home empty handed after Manchester United were pipped to the title in dramatic fashion by Manchester City.
They also exited the Champions League at the group stage and were knocked out of the FA Cup by Liverpool in the fourth round.
PSG are likely to be heavily backed by their Qatari owners this summer, having splashed over £90 million on the likes of Javier Pastore and Thiago Motta last year.
Despite their heavy spending manager Carlo Ancelotti could do little about Montpellier beating them to the Ligue 1 title, although they did at least secure Champions League football for next season.
Now Sport say they are ready to push on with their bid to make an impact in Europe next season by launching an audacious bid to land Rooney that would smash the current transfer record.
PSG have reportedly ring-fenced £120 million in order to force Manchester United’s hand, while they are also willing to vastly increase the former Everton forward's current pay packet in order to convince him to swap Manchester for Paris.
It is also reported that Lionel Messi was the French club’s first port of call before their interest was quickly rebuffed.
Rooney appeared settled at United last season after a disturbed 2010/11 campaign, during which he reportedly handed in a transfer request at Old Trafford, citing the club’s lack of ambition.