Lambert, who has scored 99 goals for the club, is the highest English scorer in the Premier League this season, leading to reported interest from others.
However, the Liverpudlian has quashed such talk, saying he would like to end his playing days at the south coast club.
"My family are happy here and I am very happy,"said Lambert.
"It has been a special three and a half years and I would love to finish my career at Southampton.
"The club's ambitions are very high. Southampton is going to be an exciting place over the next few years."