The Germany attacker is Arsenal's top scorer this season, though is recovering from a hamstring injury suffered in February.
Asked about the prospect of Havertz making their Champions League semifinal against PSG, Arteta said: "Semi-finals? I think that's too close. But if I had to bet on him earlier than expected, I would say yes.
"The way he works every day in that gym, pushing everybody, I don't think you can hold him much longer."
Arsenal meet PSG on April 29 and May 7.
Arteta also revealed on Friday he plans to experiment with Myles Lewis-Skelly in midfield ahead of the semifinal.
He added, "Yeah, for sure (confident on adapting player positions). It depends on the players as well if they are comfortable doing certain things and how we can maximise our qualities in relation to the game we expect against them.
"We have a few options and we're not going to give anything away!"