The Tottenham striker says he would like to take the armband permanently after Wayne Rooney's retirement.
"I'd like to see him scoring goals and doing what he does best as a centre forward," said Hodgson.
"It could be that the captaincy could weigh on him and in some way impact upon that.
"That will be for Gareth (Southgate) to decide, he'll have to look at those things."
He added: "I think there are a number of potential captains in the team, but one thing is for sure that he (Kane) will play the captains' type role in his position and take responsibility.
"It's up to Gareth to decide if Kane gets the extra responsibility because being captain of England is a large burden in terms of mass media and public relations duties.
"I don't know what Gareth is thinking, but there's no doubt that Kane could be a captain of England, that goes in my opinion for one or two other players as well."