Saints chiefs are reportedly considering replacing the 55-year-old in the summer, just one season into the three-year deal signed last summer. "We are lucky about this and that is the most important thing".
The Frenchman has grown unpopular with the fans due to his negative and defensive approach - their 0-0 draw with Man United on Wednesday was the fourth consecutive home game in which they have failed to score.
According to the Daily Mail, Puel has repeatedly clashed with numerous players this season, who are unhappy at his erratic rotation policy.
A review of the season will be led by club exec Les Reed next week and it's likely Puel will learn of his fate then.
"I think it's odd because someone asked me about speculation and all of the questions about how I will improve the club", Puel said.
With two games remaining in the Premier League, Southampton are aiming to finish eighth and Puel hopes to build for next season by taking six points against United and Stoke.More news: USA special counsel named to investigate Trump-Russia ties
"We have an opportunity to finish up in the table and it's a good thing after this long and hard season".
The former Monaco midfielder however, moved to play down those suggestions on Friday.
Puel said: "The last result away against Middlesbrough allowed us the possibility to finish strong in the Premier League".
"Other things I don't want to comment about".
"The League Cup final between the sides earlier in the season was a cracker, but I don't expect to see too many fireworks at St Mary's with the Saints without a home goal for 275 minutes".
"When I spoke with our opponents' players and staff, they give congratulations about our players and our quality and all of this is a good response to the speculation".