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 desperate to tie their star defender down to a long-term deal to fend off interest from abroad.
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.
And Tasci has admitted he is flattered by reports linking him with a summer switch to the Emirates Stadium or San Siro, but added that he is currently fully focused on playing for Stuttgart and helping them qualify for next season's Champions League group phase.
"I have the ambition to move clubs one day, but the time and circumstances have to be right for me," he told spox.com.
"I have to admit I'm flattered that clubs like Arsenal, AC Milan and Juventus have had their eye on me in the past.
"But I'm not getting carried away with this. I'm focused on Stuttgart and looking to return to action following my knee injury.
"I'd love to play in the Champions League this season. We'll have to show up in qualifying of course, but I don't mind who we play.
"We want to advance to the group stages. We might be paired with Arsenal, but we can beat them as well."
NEWS: Tasci yet to sign new Stuttgart deal
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