The Greek defender joined the Bundesliga club on loan last summer and has been a key part of their squad this season.
Stuttgart have kept their counsel on whether they want to keep the player for a longer period of time, but the club are interested.
They are open to the idea of extending his loan in the summer, but keeping him permanently is something the Germans are also looking at.
And according to German magazine Kicker, the Gunners are now opening up to the possibility of selling Mavropanos.
There is no clarity over whether he has a future at Arsenal and the Gunners could be prepared to let him go.
The Greek defender is happy at Stuttgart and has been enjoying his football in the Bundesliga.
It has been claimed that if Stuttgart sign him on loan again then Arsenal would be prepared to include a purchase option within the agreement.
Stuttgart are working to make sure the player stays at the club beyond the end of his current loan stint at least.