And he is under contract with the Welsh Rugby Union until 2019, incorporating that year's World Cup in Japan.
Reports had suggested that Gatland could listen to any Rugby Football Union (RFU) overtures following Lancaster's departure three days ago.
But he now joins the likes of his fellow New Zealanders Wayne Smith and Graham Henry in dismissing speculation linking him to the post.
Lancaster paid the price for England's dismal 2015 World Cup campaign, when they became the first host nation in Rugby World Cup's 28-year history not to secure a quarter-final place.
England were eliminated after just three pool games following Twickenham defeats against Wales and Australia, and RFU chief executive Ian Ritchie is leading the search for a successor who he says will be someone of "proven international experience".
South African Jake White, who coached the Springboks to World Cup glory eight years ago, remains the bookmakers' favourite, although he said on Thursday that he had not been approached by the RFU.
And White insisted the only way he would succeed Lancaster was if the RFU chased his services, and not the other way around.
"Since I finished with the Springboks I have always made it clear I have a burning desire to win another World Cup," White said.
"I can win the World Cup for England. I would never be saying that I was keen on the job if I did not believe I could do it."