The Argentine has played a huge part in the development of English talent such as Dele Alli, Luke Shaw, Eric Dier and Harry Kane and is an outside candidate for the job.
Pochettino has played down rumours linking him with the England job but said he would like to manage the Three Lions in the future.
When asked if he would be interested, he said: "Yes. Why not? In the future, yes. Not now - it's impossible".
Pochettino has also been linked with the Argentina job in the past, and says that this is also something he would like to do in the future.
"We signed a new five-year contract here but now it is not my moment; not only for England but Argentina too," he added.