There is no love lost between the London rivals at the best of times.
But that has been intensified this season as the pair compete for the Champions League places.
With the January transfer window now open both clubs will be looking to freshen things up as we approach the business end of the season.
Given the rivalry between West Ham and Spurs, players are rarely transferred between the two nowadays.
In fact West Ham co-owner David Gold even vowed never to do business with Tottenham chairman Daniel Levy again after negotiations over striker Emmanuel Adebayor collapsed last January, as reported by the Mirror at the time.
Cheeky Sullivan 'would love Kane'
With that in mind Gold's fellow co-owner David Sullivan made a cheeky joke about the chances of signing Kane during an interview with Sky Sports.
Revealing he could be set to bring in a mystery striker on loan in the next week Sullivan joked his favourite agent happens to represent the Spurs and England striker.
"It may not happen, it's just a possibility," Sullivan told Sky Sports.
"We have friendly agents and a certain agent has been very lucky for us, a guy called Will Salthouse.
"He brought us Mr (Aaron) Cresswell, he brought us the back-up goalkeeper (Darren Randolph), he brought us Mr (Michail) Antonio.
"He's got some very, very good players including the Tottenham striker... who will not be coming to us by the way because he's not for sale and we can't afford him as much as we'd love him!"
Stellar signing on horizon, but it won't be Kane
While Sullivan went on to reveal West Ham would be setting aside the majority of their summer transfer budget to try and bring in a '20-goal a season striker' it is safe to say that man won't be Kane.
The 50-goal star has recently penned a new long-term contract with the club and has been linked with the likes of Real Madrid and Manchester United, as reported by the likes of the Metro.
West Ham will be keen to bring in a stellar signing to mark their big move to the Olympic Stadium this summer.
The stadium itself has been the source of increased tension between the clubs after protracted legal challenges from Spurs over the deal which saw the Hammers win the bid to make it their new home.