That would be an agnostic position. As much as atheists protest to the contrary, atheism is a position that makes a truth claim. Now, atheism can be believed by a person while acknowledging that they don't know that there is no god, but all this shows is that they hold that position by faith. They may see evidence that they think supports their faith, but it is faith, nonetheless.
First, if they see evidence for their claim, then it's not faith - it's a rational belief. It may be wrong, their analysis of the evidence may ultimately be incorrect, but if their claim is based on empirical evidence, then it's not faith.
Second, the word 'atheist' can be defined to mean anything we want, just like any other word. So what definition should we use? Well, when someone says "I'm an atheist", the definition we should use when analysing that sentence is the definition
they use. If we use some
other definition, then we equivocate: we run the risk of saying "Aha! You said you're an atheist, and by my definition of atheism, that means you have
faith! Nyer!" - obviously, semantics cannot force someone to have faith. If the person in question genuinely doesn't have faith in anything, then our semantics therefore means squat.
We have to use the definition used by self-professed atheists, otherwise you equivocate. So, what
is the definition used by self-professed atheists? The vast majority of atheists define theism and atheism thusly:
Theism is the affirmation of the existence of deities; theists are those who make the claim "God exists". Atheists, then, are everyone else: they're those people who
don't make the claim "God exists". Atheism can be further split according a particular self-professed atheist's stance on the claim "God does not exist". An atheist who affirms this second claim is a 'strong' atheist: they reject the claim "God exists" as well as affirm the claim "God does not exist". Those who reject the second claim are 'weak' atheists: they reject both the claim that "God exists"
and the claim that "God does not exist" - they know he either exists or doesn't exist, but they don't affirm either stance. These weak atheists make up the vast majority of self-professed atheists.
Theist: Affirms "God exists" and rejects "God doesn't exist"
Weak Atheist: Rejects "God exists" and rejects "God doesn't exist"
Strong Atheist: Rejects "God exists" and affirms "God doesn't exist"
This is the definition used by the vast majority of people who say "I am an atheist". You can personally define these terms how you wish; some theists call 'atheism' what atheists call 'strong atheism', leading to confusion. Regardless, when a person says "I am an atheist", they are almost certainly implying that they are a 'weak atheist' as defined above.
As such, the vast majority of self-professed atheists do
not make a faith-based claim.