The Labour leader said he would enact this plan to “restore trust in politics”, according to The Observer.
He told his party’s peers at a meeting last week that he wants to transfer power from politicians to people by allowing them to vote on who to appoint to the upper chamber, the paper reported.
Sir Keir reportedly said: “I want to be clear that we do need to restore the trust of the public in every part of the United Kingdom in our system of government.
“House of Lords reform is just one part of that … People have lost faith in the ability of politicians and politics to bring about change, that is why, as well as fixing our economy, we need to fix our politics.”
Labour is to consult on how large the elected chamber will be, how it will be composed, and how members will be appointed before including the final decisions in its manifesto ahead of the next election.
Currently, there are 784 peers in the Lords. There are 650 MPs in the House of Commons.
Sir Keir added that the upper chamber should be “truly representative” of the UK’s nations, and that his proposals would ensure it would be responsible for amending and scrutinising bills – and not replace any of the functions of the Commons.
The pledge comes after news that Boris Johnson is seeking to hand peerages to four Tory MPs in his resignation list.
Two Johnson aides, 30-year-old Ross Kempsell, and Charlotte Owen, in her late twenties, have also been nominated, The Times said, in a report not disputed by sources close to Mr Johnson.
Earlier this month, deputy Labour leader Angela Rayner called on Rishi Sunak to block Mr Johnson’s “conveyor belt of cronies” after he proposed the Tory MPs for peerages.
Ms Rayner said: “This underhand attempt to game the system by installing a conveyor belt of cronies and skewing parliament in the Tories’ favour for decades to come should never see the light of day.
“Rishi Sunak should make it clear in no uncertain terms that he will refuse to do Boris Johnson’s bidding and reject his disreputable demands.”