In an exclusive interview the Labour leader said he was committed to "winning the argument" in the constituency following Mr Paterson's decision to stand down, after he was found to have lobbied ministers and officials on behalf of two firms that were paying him.
Former Herefordshire and Shropshire MEP David Hallam is understood to be on a shortlist of potential candidates that also includes former Telford & Wrekin Council leader Kuldip Sahota, and Graeme Currie, the Labour candidate for North Shropshire in the 2019 general election.
Sir Keir is attempting to capitalise on the sleaze row, which he says has seen Boris Johnson treat the public with "contempt" and has "trashed" the reputation of British politics.
He wants to do in Shropshire what the Tories did in the Black Country in 2019, by defying the odds and winning a seat that has previously been out of reach.
He told the Star: "We're going to fight to win everywhere, including in North Shropshire.
"The local constituency party will decide the candidate pretty quickly, but I'm a great believer in having people from the locality standing.
"I'm well aware that in order to persuade people to look again at Labour and then hopefully to vote for Labour, I have to show why it matters to me, which is why I want to be among the communities where we want to be winning the argument."
Kirsty Walmsley, the daughter of a former Shropshire Council leader who switched from the Conservatives to Reform UK, is the first confirmed candidate in the by-election.
Meanwhile a spokesman for the Conservatives said members of the North Shropshire group would choose their candidate.
He said: "The local Conservative Party members will select a candidate for North Shropshire in due course."
To win the by-election, which is likely to take place next month, Labour will need to overturn a majority of 22,949.
Sir Keir has also hit out at the possibility of Mr Paterson receiving a peerage. "It would pile corruption upon corruption," he said. "And I think there would be a revolt in the Lords.
"It would be absolutely the wrong thing to do."
Mr Paterson has denied any wrongdoing.