Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
The 26-year-old joined from St Etienne in 2011 and his deal was due to expire this summer, but it was widely anticipated that talks would result in him agreeing to stay on with the fast-progressing capital club.
PSG announced on their official website: "Paris St Germain are happy to announce a four-year contract extension for Blaise Matuidi. The France international is therefore tied to the club until June 2018."
Matuidi, a combative key member of the PSG midfield who has played 19 times for France, said: "I was absolutely wishing to extend my adventure with Paris St Germain. The unlimited ambition of the club has no equal in Europe."
Club president Nasser Al-Khelaifi, the Qatari businessman whose takeover at the end of 2011 has driven PSG's emergence as a major European force, welcomed news that Matuidi would remain in Paris.
"Blaise Matuidi wants to make a permanent mark on the history of Paris St Germain," Al-Khelaifi said.
"We are sending a very strong signal in France and in Europe by extending the stay of one of the best French players. Together we want to build one of the best clubs in the world."
PSG again head the French Ligue 1 standings this season, and stand on the brink of reaching the Champions League quarter-finals after a 4-0 victory at Bayer Leverkusen in the first leg of their last-16 tie.