The 31-year-old has scored two goals in three games for the Three Lions after making his debut back in August.
Lambert, who has been included in the squad for the upcoming World Cup qualifiers against Montenegro and Poland, insists that he will keep working hard in order to secure a place at next year's tournament in Brazil.
"There's a lot of things that have got to happen between now and then," he told The Mirror. "I'll just keep working hard.
"I've never taken anything for granted. And if that chance does come then, yes, I will take it."
Lambert has scored two goals in seven appearances for Southampton this season.