The German international had initially been ruled out for the campaign after having surgery on the injury suffered during a Dubai warm-weather training camp in February.
Arsenal have survived the loss of both Havertz and Gabriel Jesus to make the Champions League semi-finals for the first time since 2009 with a famous 5-1 aggregate victory over Real Madrid.
Arteta cooled speculation Havertz could return in time to face Paris Saint-Germain in the last four.
But he is on track to be available should Arsenal get the final in Munich on May 31.
“For the semi-finals? I think that is too close,” said Arteta.
“But if I have to bet on him (being available) earlier than expected I would say: ‘Yes’.
“The way he works, every day he is in the gym, pushing everybody, and I don’t think you can hold him back any longer.”
Arsenal’s European run has softened the blow of seeing their Premier League title challenge peter out.
The Gunners are on course to finish second for a third consecutive season.
But they trail Liverpool by 13 points with just six games remaining.
The title could be sealed as early as Sunday should Liverpool beat Leicester and Arsenal lose at struggling Ipswich.
Arteta is keen to avoid that scenario and warned against easing up in the league with Champions League qualification for next season not yet confirmed.
“We’ll make sure that we win the game and that doesn’t happen,” added the Spaniard on the possibility of Liverpool winning the league on Sunday.
“We need to step up and start to win the games.”
By AFP
