What is the meaning of 「って」 in this context?


I have scoured every article and every related answer in this forum that I can
find, but even so I preemptively offer my apologies if this is covered
elsewhere. I'm an intermediate Japanese learner, and came across this usage of
って in a manga I'm reading (Death Note - 1):

> 死神がこんな事言うのもおかしいが生きてるって気がしなくてな...

The translation I came up with is " **It's funny that a god of death would say
this, but I just didn't feel alive** ", which seems correct given the context.
However, I can't figure out what grammatical purpose the って is serving in
「生きてるって」. Can someone explain its usage here?

