As recently as June, the Gunners revealed that Hein had agreed to sign a new one-year contract having initially been free to depart on a free transfer.
Since 2018, Hein has made just the one senior appearance for the club, featuring in an EFL Cup third-round defeat to Brighton & Hove Albion in September 2022.
The initial expectation had been that the Estonia international would jump at the opportunity to move elsewhere in search of first-team football.
However, despite having made a total of just four outings in Premier League 2 and the EFL Trophy during 2023-24, there now appears to be a plan in place for his development.
Arteta open on Hein future
With David Raya and Aaron Ramsdale enjoying a break after representing Spain and England at Euro 2024, Hein got his opportunity to impress in Wednesday's pre-season friendly against Bournemouth.
Hein took his chance, saving penalties from Philip Billing and Ryan Christie to help Arsenal win a shootout after the two sides had played out a 1-1 draw in the United States.
Post-match, Arteta was naturally quizzed on his thoughts about the goalkeeping situation at Arsenal, acknowledging that a loan exit is a distinct possibility.
As quoted by the Evening Standard, the Spaniard said: "That's a conversation that we are having at the moment. Obviously, David and Aaron are away at the moment and we're really short in the position.
"We want to develop our players, especially a player like Karl with a big potential and a big future ahead of him. He needs to play games, so we're going to explore that option as well."
Could the situation change?
In recent weeks, Arsenal have been credited with an interest in Wolverhampton Wanderers stopper Daniel Bentley, who spent part of his youth career with the club.
Should that deal eventually go through, the expectation is that Bentley would take on the role of third choice behind Raya and Ramsdale.
That said, it is an open secret that Ramsdale would prefer to leave Arsenal having lost his place to Raya. As it stands, no club has been prepared to meet the England international's asking price.
If Ramsdale did leave Arsenal, the Gunners would be unlikely to make Hein or Bentley the chief deputy to Raya, leaving Arteta to re-enter the market for yet another goalkeeper.
Tommy Setford has recently arrived from Ajax, but the 18-year-old will start life at Arsenal in the academy ranks.