The north London side are being increasingly tipped as potential Premier League winners this season after losing just twice in their opening 20 top-flight games.
If they get rid of the manager or Kane, it says to me they have no real ambition
However, Tottenham striker Kane has been linked with a move to Manchester United regularly over the past 12 months, whilst Pochettino has been touted as a potential replacement for struggling Louis van Gaal at Old Trafford.
Although Wright believes Tottenham are on the cusp of something special at The Lane, the former Arsenal striker warned Spurs chairman Daniel Levy that he can ill-afford to lose two of their key men.
“Tottenham might have a problem soon,” Wright told BBC Radio Five Live.
“Kane is going to continue what he’s doing. Pochettino is going to be a success there. Spurs are doing the right thing. I believe Spurs have something happening.
“If they get rid of the manager or Kane, it says to me they have no real ambition.”
Kane has scored 11 times in 20 Premier League games for Tottenham so far this season.
Former Argentina international Pochettino was appointed as Tim Sherwood’s permanent replacement in May 2014 after impressing during a short stint in charge at Southampton.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news