The Ligue 1 champions are chasing a replacement for Carlo Ancelotti, who has made clear his intention to join Real Madrid this summer.
The likes of Fabio Capello and Andre Villas-Boas have already turned down the capital club and Rijkaard's representative says his client is not interested in coaching a club in the coming campaign.
“It’s a fantastic project there in Paris and I can imagine it’s a beautiful job for any coach, but it’s as simple as I already stated: Frank doesn't want to train a club this year,” Perry Overeem told Goal. "It doesn't matter which club comes by, it will not happen."
Rijkaard has been out of work since being sacked as Saudi Arabia boss back in January. He won the UEFA Champions League as a player with Ajax in 1995 before guiding Barcelona to the title as a manager in 2006.
PSG has also been linked with a move for former France coach Laurent Blanc, who has been out of work since the end of Euro 2012.