Rooney is out of England's final two qualifiers with an ankle injury, and although Walcott also wants to play as a central striker, it appears Hodgson prefers Kane and will continue to play the Arsenal forward out wide.
"This is a big opportunity for him (Kane)," Hodgson told reporters.
"He's got a good career ahead of him, so it's a nice he'll get an opportunity. With Wayne out, he's in pole position," the manager added.
Walcott, who has played mainly on the right wing in his career, has impressed in a central role for his club this season, scoring 12 goals in his last 14 Premier League starts.
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Hodgson says he hopes Walcott, who missed the 2014 World Cup with a knee injury, can show the same kind of form for his country.
"I don't think it's a big debate whether he (Walcott) starts up the centre or on the right or left. What we're asking him to do is what he does for Arsenal with Alexis Sanchez," the 68-year-old said.
"Since coming back from the latest injury and having a chance to start a few games for Arsenal, he's shown the qualities he has.
"We hope he does for us what I've seen him do for Arsenal," Hodgson added.
England have already qualified for next summer's finals in France, winning all their eight games so far. They travel to face Lithuania on Oct. 12 after the Estonia game at Wembley.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Amlan Chakraborty)
