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Spurs are looking for a permanent successor to Jose Mourinho, who was sacked after just 17 months with the club all but certain to finish outside the top four for another season.
Player-turned-coach Ryan Mason has been put in charge for the remainder of the season, and on Friday said he is open to working for the new man in charge next term.
The identity of which remains unknown, with Spurs understood to be drawing up a list of candidates before any approach is made. An announcement is not expected before the end of the season.
Kane, meanwhile, has three years remaining on his contract and Spurs have ruled out a sale this summer amid reports the player contemplating his future after another season without a trophy.
Merson believes any new manager will need reassurances that Kane is staying before taking the job.
He wrote in his Daily Star column: "Tottenham still can’t find a new manager. But it’s not a great job that one, is it?
"No disrespect to Spurs. I’ve played against them many times in my career. I know what they’re about. They’re a good club. A class club. With a great stadium.
"But if I’m a top manager looking at it from the outside, I’m thinking: 'What’s happening with Harry Kane?' Any plans you make go out the window on day one if Kane leaves Spurs - and it sounds like he might.
"The thing is, if Kane leaves Spurs, others will too. That team could break up. So it’s just not that attractive a job right now because of all the uncertainty.
"Look who’s failed there in recent times too. Mauricio Pochettino is a great manager. Couldn’t win there. Jose Mourinho is one of the greatest ever, and he struggled. I can see why managers are not exactly queuing around the block.
"Spurs might have to give Harry Kane a new contract. Throw money at him to stop him leaving. Otherwise it could be hard to bring in a new manager."