Bobby Charlton will present Wayne Rooney with a golden boot for surpassing his England scoring record prior to kick-off, but with the Manchester United striker ruled out of both Friday's game and Monday's trip to Lithuania with a minor ankle problem, it is Kane who will spearhead the team.
Hodgson was caught on camera smiling broadly at White Hart Lane last month after Kane scored his first club goal of the season in Tottenham Hotspur's 4-1 win over Manchester City and he has challenged the 22-year-old to prove himself a capable deputy for 29-year-old Rooney.
"It's a big opportunity," said Hodgson, whose side have already qualified for next year's tournament in France and are seeking to complete Group E with a perfect record of 10 wins.
"He's waited a long time for his chance, not least through the Under-21 championship, but when he got his chance he scored with his first touch of the ball (in England's 4-0 win over Lithuania last March).
"It's now, this autumn, that we have him exclusively to ourselves. We believed in him. He's got a good career ahead of him, so it's nice he'll get an opportunity.
"With Wayne out, he's in pole position. He has competition from other players, but he is in pole position."
Hodgson confirmed that Kane will line up in Rooney's central role, with Arsenal's Theo Walcott, Manchester City's Raheem Sterling and Jamie Vardy of Leicester City among the players vying for position on the flanks.
Uncapped Liverpool forward Danny Ings and Swansea City midfielder Jonjo Shelvey are injury doubts, but Hodgson revealed that Rooney's United team-mate Michael Carrick will anchor the midfield in the absence of the injured Jack Wilshere.
"The way we try to play, and the role that Jack Wilshere has played in a central playmaker role, getting hold of the ball and starting the play we want to see, Michael Carrick is very similar," Hodgson told reporters at England's team hotel in Watford, north of London, on Thursday.
"Not similar players, but he plays a similar role and can do a similar job. So in the absence of Jack, I'd like to see Michael doing the job. We believe he can."
- Cahill captain -
Tottenham's 19-year-old midfielder Dele Alli could make his senior international debut after receiving his first call-up, while Chelsea centre-back Gary Cahill will captain the team in Rooney's absence.
"I will approach the game like I would any game," said Cahill.
"But it's something I'm very proud about. It'll be a special day and I want to enjoy it as much as I can."
Though unfit, Rooney will attend the match in order to receive the commemorative boot from 1966 World Cup-winner Charlton, whose record of 49 goals he surpassed with a late penalty in last month's 2-0 win over Switzerland.
A giant flag bearing a picture of the England captain will also be passed around by supporters.
With two matches of the qualifying campaign remaining, Estonia remain in contention for a place at next year's tournament in France, but they have little margin for error.
They trail Slovenia by two points in the scramble for third place, which will yield a play-off berth, and if Slovenia defeat Lithuania on Friday and Estonia fail to beat England, Magnus Pehrsson's side will no longer be able to qualify.
"The chance is tiny and we face two great challenges," said Pehrsson, whose side finish their campaign at home to Switzerland.
"We need to win at Wembley and at home against Switzerland to make it. We'll need to prepare ultra well and produce a fantastic performance. Then the chance we've been working for will open up."