Hart is currently on loan at Serie A club Torino after being shipped out of Manchester City by Pep Guardiola at the start of the season.
Claudio Bravo has drawn heavy criticism for his performances as City's first-choice goalkeeper but Hart's future under Guardiola beyond the end of the season is still uncertain.
Arsenal goalkeeper Petr Cech also came under fire last week for his role in Chelsea's third goal in Arsenal's 3-1 defeat.
Arsene Wenger isn't interested in signing Joe Hart at Arsenal
Joe Hart is currently on loan at Torino from Manchester City
And this week it was reported that Arsene Wenger wants to bring in Hart as Cech's long-term replacement.
But the Arsenal boss insists he has no interest in signing Hart and claims the club is fully stocked in the goalkeeper department.
"I have three world-class goalkeepers and I'm very happy with the three I have," said Wenger.
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Colombia international David Ospina has not featured in the Premier League this season but has been used as Arsenal's No1 goalkeeper in the Champions League.
Arsenal also handed third choice goalkeeper Emiliano Martinez a long-term contract while Wojciech Szczesny is out on loan at Roma.
Another player on loan who's future is currently uncertain is Jack Wilshere.
Arsene Wenger also said Bournemouth haven't made contact over a permanent deal for Jack Wilshere
The England international is currently with Bournemouth but Wenger fully expects to have Wilshere back at Arsenal in the summer.
"We have, at the moment, had no move from Bournemouth for Jack Wilshere."