Sky Sports' Kaveh Solhekol relayed the news:
Sky Sports News added Arsenal intend to have Arsene Wenger's replacement in the hot seat before the 2018 World Cup, which kicks off on June 14.
Though Arteta—who was spoken to on Thursday—is said to be the front-runner for the position, the club will speak to Henry and other candidates as part of an "extensive process" to find Wenger's successor.
Henry scored 228 goals in 377 games for Arsenal, but like Arteta, he has no senior management experience.
The Frenchman has served as assistant coach to Belgium national team boss Roberto Martinez since 2016, while the Spaniard has performed the same role under Manchester City manager Pep Guardiola.
Henry recently displayed his new insight into the coaching side of the game while paying tribute to Wenger, per Arsenal's official Twitter account:
Appointing him would carry many of the same pros and cons that hiring Arteta would bring—either would be a young, exciting choice who could bring fresh ideas into the club, which they know well, but their lack of experience makes it difficult to assess how successful they might be.
Arteta perhaps has the advantage in terms of having worked under arguably the world's best coach in Guardiola, and that could be a factor in Arsenal's thinking.
They'll have a clearer sense of who they feel would be a better choice once they've spoken to Henry as well, so there could be more developments once those talks have taken place.