Bayern Munich forward Toni Kroos left the door open for a switch to the Barclays Premier League in the summer.
Tim Sherwood claims the "silence is deafening" from the Tottenham board amid speculation he could be replaced as manager.
The Ivory Coast player penned a new deal at the end of the 2011-12 season, having mainly worked as a full-back in his first six years with Stuttgart.
But the 30-year-old's success as a central midfielder for much of last season has led to the German outfit's desire to extend his stay.
Boka rejected a move to Tottenham in 2009, and with his current deal expiring in 2014, Stuttgart are keen to retain his services rather than see him leave for free.
"The way Artur Boka performs on his new role inside the first team is a definite plus for us," said Stuttgart's general manager Fredi Bobic.
"I do not see any reason why he should not be staying on longer than the end of his current deal.
"We will absolutely have talks with him about a new contract."