The 38-year-old discussed a move before flying to Mallorca with the Germany squad to begin their Euro 2008 preparations.
It is believed Lehmann wants to sort out his future before next month's European Championships in Austria and Switzerland.
Stuttgart require a new goalkeeper after Raphael Schafer, who was signed from Nurnberg last summer, failed to live up to expectations.
However, general manager Horst Heldt told Germany's Bild newspaper he will not be held to ransom in his bid to sign Lehmann.
"If he wants to earn as much as he did at Arsenal, then we have no chance," said Heldt.
Stuttgart, who finished sixth in the Bundesliga, are thought to be offering a one-year contract, with an option for a second year.