Lindsay Lohan isn't offended that The Wanted singer Max George completely denied their relationship on Twitter this week -- because as far as she's concerned, there IS no relationship ... they're just hook-up buddies.
Lindsay posted the above photo on Instagram a few days ago -- showing her and Max joking around together -- and Max's fans erupted on Twitter ... writing things like, "If you date Lindsay, I will die!"
Max responded to the complaints, flat-out denying he was dating Lindsay whatsoever -- and called speculation about their relationship "rumors ... That's all ... Like I said ... 1 million percent."
But Lindsay's telling friends, she doesn't feel burned -- because Max is telling the truth ... they aren't boyfriend and girlfriend ... they just have a no-strings-attached non-exclusive hook-up thing going on.
We're told Lindsay is not taking things seriously with Max at all -- she just likes hanging out with him -- and he's free to tweet whatever he wants.