Harry Kane will stay at Tottenham as long as they are competitive
Kane has been in stunning form for Tottenham this season after a dry August.
He has scored 15 goals in his last 10 games for club and country and was short-listed for the Ballon d’Or this week.
The 24-year-old is happy at Tottenham and the club are not willing to discuss a sale, but Real Madrid have been linked with a move worth £200m.
But Anderton thinks he’ll stay as long as Tottenham are competing for the title.
They finished second last year and have started this campaign well despite struggling at Tottenham.
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Harry Kane captained England against Slovenia this week
"You hope he's Tottenham through and through," Anderton told Press Association Sport.
"The way he plays and the way he acts, it certainly looks like he's happy where he is and hopefully he doesn't forget that.
"I think he'll want to complete his journey at Tottenham. He'll want to play in that new stadium and he'll want to be part of the Tottenham team that wins the league.
"But the club have got to go with him on that. If the offer comes in from say Real Madrid, it will be up to Spurs to turn it down. If you look at his age, his talent, the way he is, he's got to be worth around £150million, even £200million now.
"If they say yes, Harry will get the chance to speak to them and I'm sure if he walks into the Bernabeu with an opportunity to sign, he'd find it very difficult not to. And would you blame him? You couldn't, absolutely not."
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Kane has collected the Premier League's Golden Boot award for the last two years in a row but appears to be reaching even greater heights this season.
He has five goals from Tottenham's opening two Champions League fixtures while successive winners for England, as captain, have secured victories over Slovenia and Lithuania in the past week.
Anderton is backing Kane to be made permanent England skipper and says the forward's performances remind him of how Alan Shearer used to lead from the front.
"Harry can score a goal from any situation and as players you like to see someone leading the line," Anderton said.
"For me, seeing Alan Shearer at Wembley smash someone like Scotland's Colin Hendry in a big game, it gave us that buzz. You see your team-mate like that and you think, 'We're winning this, we're up for this'.
"I think Harry Kane is that sort of player for Tottenham and England, and with him having the captaincy, it will take him even further forward.
"He's still young but I think the players look up to him. I think he would be a good pick."
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