Newcastle are looking for a new manager after Keegan resigned last week in the wake of a dispute about the control of player transfers.
"All I intend to do is relax and continue with my job," Poyet told Tottenham's website, who returned to Spurs in a coaching capacity in October 2007 having played for the club for three seasons between 2001 and 2004.
Wise has been linked with a return to management with Newcastle, while Alan Shearer, David Moyes and Didier Deschamps have also been mentioned as possible contenders.
Carling Cup holders Spurs are due to play Newcastle at St James' Park in the third round of the competition on Wednesday 24 September.
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