According to Spanish publication Don Balon, PSG bosses are fed up with Real Madrid’s attempts to unsettle Neymar and want revenge.
It is claimed the French club have contacted Kroos’ agent to test the water ahead of a summer swoop.
They are reportedly willing to pay €200million (£173m) to seal a deal.
Don Balon say PSG plan to double Kroos’ current pay packet and hand him a five-year contract.
However, the Germany international’s agent reportedly told PSG to back off until the end of the season.
Kroos has three seasons left on his contract with Real Madrid.
He joined Los Blancos from Bayern Munich in 2014 and has helped the team to two Champions League titles and one La Liga crown.
Despite being rated as one of the leading midfielders in European football, Kroos has been linked with a move away from the Bernabeu this summer.
Kroos has also been linked with a move to Manchester United.
Real Madrid president Florentino Perez is reportedly plotting a revamp of the squad after a disappointing domestic campaign.
Perez is said to be desperate to land Neymar from PSG but needs to raise the funds to pull off such a deal.
