Kane, who scored four goals during England’s Euro 2020 campaign, informed Spurs of his desire to leave the club earlier in the summer.
Premier League champions Man City have emerged as the frontrunners to sign Kane as they look to replace Sergio Aguero, who has joined Barcelona, but Man United and Chelsea have also been linked with moves.
But former England defender Mills believes Liverpool, who finished third in the top-flight last season, should enter the race for Kane’s signature and says he would be ‘perfect’ at Anfield.
‘Liverpool should look to sign an out-and-out centre-forward,’ Mills told talkSPORT.
‘Harry Kane would suit them perfectly with the way he plays in that slightly deeper role, the nine-and-a-half position, where he drops in from time to time.
‘If you had Sadio Mane going down one side, Mo Salah going down the other, Kane in the middle – the chances he would create for them and himself would be perfect.
‘He’s not going there, I don’t think. But it would be the perfect fit.
‘Son is a fantastic player, but playing with two quality players either side of him, with Diogo Jota there as well, that would be unbelievable for Kane.
‘In terms of a fit, that’s the best fit. Do I think he’ll go there? No.’
Despite Kane privately and publicly suggesting he will leave Tottenham this summer, new Spurs boss Nuno Espirito Santo recently said he had ‘no doubts’ over his commitment to the club.
‘I have no doubts in my mind. What I wish is for Harry to recover well and have a good rest,’ said Nuno, speaking at his first press conference since his belated appointment as Jose Mourinho’s permanent successor.
‘When he arrives he will feel that he has to commit himself to become better. We are ambitious, we want to do well and we count on Harry to do that.
‘Harry is our player, period. There is no need to talk about anything else. Now is the time for him to rest. When he returns we can have a good conversation. I am looking forward to him joining the group.’
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