The Turkish-born German international, 23, has made more than 100 league appearances for the Bundesliga side since breaking into the first team in 2006 and was part of his country's squad that reached the semi-finals of the World Cup.
Tasci was the last outfield player in Germany's squad to be fielded during the tournament in South Africa, coming on as in injury-time substitute against Uruguay in the third-placed play-off.
As well as the Gunners, Tasci has also reportedly attracted interest from Arsenal's arch rivals Tottenham Hotspur.
However, a source close to the player has claimed that the centre-back is only willing to swap the Mercedes-Benz Arena for Emirates Stadium if Wenger came calling.
"He has a long term contract but if Arsenal made an offer he would consider it. They are a great club wtih a great manager, but there is no contact at the moment. Tottenham have shown interest, but not Arsenal," the source told Sport.co.uk.
Tasci’s agent, Uli Ferber, had previously hinted that were the defender to leave Stuttgart, Arsenal would be the likely destination.
"Serdar admires English football and has huge respect for Arsenal," he said in The Sun.
Tasci is believed to have an £18.5 million buy-out clause in his contract, and has also been linked with Juventus.
Wenger is on the lookout for another central defender, with only Thomas Vermaelen, Johan Djourou and new signing Laurent Koscielny in his ranks having seen Sol Campbell, William Gallas, Mikael Silvestre and Philippe Senderos all depart over the summer.
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