The South Coast side are believed to be eyeing up the Dutch international stopper.
De Telegraaf report that Southampton are hoping to sign the Dutch international goalkeeper, who is currently on loan at AS Monaco.
Southampton boss Ronald Koeman managed Stekelenburg at Ajax, so the pair know each other well, and it is a deal that would make sense.
Fraser Forster has broken his kneecap and could miss the start of next season, so action needs to be taken now to sufficiently cover his absence.
Stekelenburg is a World Cup finalist with Holland and has over 50 caps for his nation. However, his career has gone down the pan since leaving Ajax for Roma in 2011. He soon became second choice in the Italian capital. He left for Fulham, but struggled and played less than 20 times for The Cottagers before losing his place in the team, first to David Stockdale then Jesse Joronen and Marcus Bettinelli.
This season he has sat on the bench on loan at Monaco, with Daniel Subasic ahead of him in the pecking order.
There is no word in the report of when a deal could happen. Stekelenburg has a contract at Fulham until 2017, so an early release from that deal seems unlikely. Instead it is likely to be a deal that would go through this summer.