The longer negotiations drag on, the more likely an exit from the reigning Ligue 1 champions becomes.
Speculation in France suggests a deal is close, with Matuidi set to prolong his stay in the capital until 2018.
PSG need to move quickly , though, if they are stop the vultures from circling, as the 26-year-old midfielder will be free to discuss pre-contract terms with interested parties in the new year.
Chelsea and Manchester City are among those said to be waiting to pounce, with Matuidi having figured prominently on Premier League radars for some time.
The France international claims 'anything can happen' from this point, but would be prepared to shun interest from afar if a suitable offer is put to him in Paris.
Matuidi told L'Equipe 21: "I am really at ease at PSG.
"My first wish would be to stay. But you can wish for something and sometimes it doesn't happen.
"The club has a special place in my heart, but anything can happen in a career."