The 28-year-old joined Southampton from Nice in August 2016 after deciding to leave France on a free transfer.
However, he has only made three league appearances after suffering a cruciate ligament injury in his first campaign.
Claude Puel then left the club in the summer after signing him and Pellegrino has looked at other options in the first 15 games of the season.
Pied admits his career on the south coast has been a disaster so far but he has refused to give up at St Mary's.
He told the Daily Echo: "It was the decision of Southampton Football Club, so I have to respect that.
"I have a contract with Southampton and I have to respect that.
"It doesn’t matter what's in my head, for me when I have a shirt I give 100 per cent for the shirt. Of course, I signed with Claude Puel but if it’s another manager this is part of a professional footballer’s life.
"We have to respect and just give your maximum on the pitch."