The 28-year-old enjoyed a lengthy run in the Fulham side towards the end of last season, as he was preferred to Holland international Maarten Stekelenburg.
He impressed despite suffering relegation out of the Premier League and has seen his efforts noted elsewhere.
Stockdale has always maintained that his ambition is to be the number one at Fulham, having taken in several loan spells since moving to Craven Cottage in 2008, but he now has just 12 months left to run on his current contract.
His possible availability has sparked interest from afar, with a number of clubs ready to test Fulham’s resolve.
Brighton are said to be leading the hunt as they seek a replacement for the departed Tomasz Kuszczak.
A £1million offer is said to be in the pipeline, but Magath is staying tight-lipped when it comes to possible transfer talks and intends to leave the matter in the hands of his chief executive.
He said in the Fulham Gazette: “You have to ask Alistair (Mackintosh).
“We have four goalkeepers and that situation I’m very happy with.”