The Brazilian defender, whose current contract runs out in 2015, has silenced reports linking him with a move to Serie A by verbally pledging his future to the Ligue 1 champions
In recent weeks the Brazilian centre-back, 31, had been linked with a summer switch to AC Milan or Napoli as his contract runs out in June 2015.
However, Alex has shut the door on the rumours by confirming his future remains at Parc des Princes.
"My career here can last for several years," les Parisiens defender told beIN Sport.
"I hope to renew the contract as soon as possible. I want to finish my career here."
Alex joined the reigning French champions from Chelsea in January 2012, helping them to the Ligue 1 title in his first full season at the club under Carlo Ancelotti, and has remained a prominent figure in Laurent Blanc's set-up this season.