Thauvin flopped after his £13million move from Marseille last summer, lasting less than six months at St James's Park.
He returned on loan to Marseille in January and finished the season strongly, while back on Tyneside, Newcastle were relegated from the Premier League.
The winger admits it was 'painful', and hinted that he doesn't want to return to Newcastle to play in the Championship.
But he stressed that talks with the club will remain private as he is linked with another season-long loan to Marseille, while Lazio are also reported to be keen on his services.
Thauvin said: “My agent has had discussions with the club and continues to have them. Newcastle have always been professional with me.
"This is a legendary club in England who did not deserve to go down.
“I thought about my team-mates and fans after relegation. It was painful. I know what I want. We continue to discuss with the club what happens next, but this must remain between us.
"I greatly respect Newcastle and its leaders too much to speak publicly on the situation.”
Thauvin, speaking to La Provence, admitted a return to Marseille was a possibility, but also said his agent had been in contact with other clubs.
He added: “I know that Marseille thinks that. I have said again and again, Marseille will be special in my life, this club has a big place in my heart.
“Obviously, we can not remain indifferent to that interest but it is for Newcastle or Marseille to communicate on that subject.
"My agent is in contact with several clubs, that’s not for me to speak. For now, I am a Newcastle player.”