The Labour leader said the 53 countries of the association should choose who succeeds the Queen, suggesting the holder of the post could be decided on a rotational basis.
Mr Corbyn earlier told the same programme: “I think the Commonwealth ought to really get a chance to decide who its own head is in the future.
“The Queen clearly is personally very committed to the Commonwealth but after her I think maybe it’s a time to say well actually the Commonwealth should decide who its own president is on a rotational basis.”
Commonwealth secretary-general Baroness Scotland of Asthal, asked about Mr Corbyn’s comments, told ITV’s Peston on Sunday said: “Fifty-three heads of government are the heads and they will make a decision in whatever way they determine.”
Lady Scotland sidestepped questions over her personal preference, reiterating it was for the member countries to decide.
The trio’s remarks came before the Commonwealth Heads of Government Meeting (Chogm), which starts on Tuesday in London.
Mr Johnson also dismissed suggestions the government should apologise for wrongs carried out by the British state to other Commonwealth countries.
He said: “That hasn’t been suggested to me by any Commonwealth leader, foreign minister or sherpa of the summit that I’ve met so far.”
Mr Johnson added: “It’s not a proposal that, as I understand, carries much support amongst the 53.”
Mr Corbyn had said it is very important that Britain recognises its “historical role in many of these issues”, including the treatment of people in Kenya during the Mau Mau uprising.
He said: “There’s been a sort of apology given on that.
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“On the Chagos Islands, it’s an issue I’ve been very closely involved with for a very long time, that is going to come up at Chogm, no question about that, and I think it’s important the British government just recognises what Britain did with the Chagos islanders was immoral, was wrong and brutal.
“Put it right and give them their right of return.”
Chagossians were forced to leave the central Indian Ocean territory by 1973 to make way for a major United States military base on Diego Garcia, the largest of the islands.
This agreement with the US secured a discount on the Polaris nuclear weapons system for the UK.
The expulsions are regarded by some as one of the most shameful parts of Britain’s modern colonial history.