The Daily Mail report claims that the side from the French capital have targeted the Anfield forward after missing out on other big names.
Liverpool boss Kenny Dalglish would be loath to let the Uruguayan go in the summer after coming under such flak for defending him through the various ups and downs of the race row with Manchester United’s Patrice Evra.
Suarez joined the Merseyside club just a year ago but PSG will have no problem meeting any Liverpool asking price – they have already shown their intentions with a number of big money signings.
Suarez has just returned to action after seeing out an eight-match suspension for racially abusing Evra at Anfield and the incident as a whole has led to him being subject to much public ire.
The report suggests the interest from Paris could tempt him to escape the bad press and join compatriot and friend Diego Lugano.