The Frenchman, who signed a three-year deal last summer, told Sky Sports News ahead of Wednesday's Premier League meeting with Manchester United: "I cannot be distracted about the speculation.
"The most important thing is to think about finishing strong in the Premier League. After that, I cannot make comments about speculation.
"I'm on contract, a three-year contract, with a project. I am happy here, with the directors, the staff and the players but the most important to continue to improve.
"There's no need to give assurances because it matters about what is on the pitch with the quality. It's the second-youngest team in the table and we continue to improve for the future."
Puel took Southampton to the EFL Cup final in February and will secure an eighth-place finish in the league if they win their final two games.