For now, the former Chelsea manager is contracted to the FA to the end of next year's World Cup.
Tuchel declared on Friday: "If everyone, the FA is happy with me, there's always the possibility (to stay on), but the focus is now for this camp.
"It's a lot of fun, especially since we're on track in the last two camps. There is nothing to announce at the moment, but I'm very happy with the way things go. I think the federation is quite happy with the way things are, but I have to prove myself here. The rest will take care of itself.
"I'm in a good place mentally because I love the team. I love the support from the federation and I love the direction where it's heading. We have time for it (a new contract)."
England, having already qualified for the World Cup, will face Sweden and Albania in dead rubbers next week.