The French Ligue 1 outfit are backed by the wealthy Qatar Investment Authority and the newspaper L'Equipe understands the club will make a bid for the player at the end of the season.
The Reds striker has become a firm fan favourite at Anfield ever since his €26.5 million move from Ajax to Liverpool over a year ago, but more recently he has endured an emotional draining season blighted by suspensions and a well-publicised spat with Manchester United defender Patrice Evra.
The Uruguayan was found guilty of racially abusing Evra during a hot-tempered clash between United and Liverpool late last year and as a result was banned for eight games.
Suarez then incited more controversy upon himself when he refused to shake the hand of Evra when the two English sides met again last Saturday.
Liverpool managing director Ian Ayre would later accuse the forward of letting the club and its manager Kenny Dalglish down for his actions.
As a result, L'Equipe reports that the player is available in the summer and that PSG plan to use Suarez's Uruguay teammate Diego Lugano, who is at the French side, to help persuade the 25-year-old to make the move to Paris.
PSG currently sit top of the Ligue 1 table and it looks likely that they will be able to offer UEFA Champions League football as an attractive lure to get Suarez over next season.
Liverpool, on the other hand, currently sit seventh in the Barclays Premier League.
However, this is not the first time a high profile player like Suarez has been linked to PSG with a move failing to materialise in the end including David Beckham, Alexandre Pato and Carlos Tevez.