The Defence Secretary has previously positioned himself as a candidate as the military alliance’s current secretary general Jens Stoltenberg’s term is expiring in September.
It's not for me to decide. It's for all the other allies
Mr Wallace told German news agency dpa: “I’ve always said it would be a good job. That’s a job I’d like.
“But I’m also loving the job I do now. I mean, to be Defence Secretary of the British Government at a time of reform and investment, just like Boris Pistorius.”
He added that secretary general of the transatlantic alliance “is a fantastic job and Nato is an incredibly important part of all our securities”.
“But it’s not for me to decide. It’s for all the other allies.”
The race for the top job has been heating up, with Mr Stoltenberg indicating he will not seek a further extension after nearly a decade in the role.
Nato member states typically decide on the alliance’s next chief behind the scenes.
Mr Wallace would have to overcome the opposition of those said to be pushing for a woman or someone from eastern Europe, and of France, which would reportedly prefer an EU candidate.
If the Defence Secretary did succeed, it could trigger a by-election in his Wyre and Preston North seat, although it is set to be carved up under a planned shake-up of Westminster constituencies later this year.
The appointment of Labour MP George Robertson as Nato chief in 1999 led to a by-election in his Hamilton South constituency, south west of Glasgow.