The 22-year-old defender, who accumulated seven international caps over the past year, is believed to be a target for AC Milan and Juventus as well as the Gunners.
And with interest in Tasci high, Stuttgart are determined to tie their star defender down to a long-term deal to fend off interest from abroad.
However, with his current deal set to expire at the end of next season, the club are yet to agree a contract with the player to secure his services until 2013.
"We have not reached anything close to an agreement as yet," a club spokesman told Stuttgarter Zeitung.
"Talks are ongoing, of course, but there is nothing that will be announced soon."
Tasci has made 74 league appearances for the German outfit since breaking on to the first-team scene in 2006, and can operate at both right-back and in the centre of defence.
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