Amanda Milling said she expected a "very tough battle" in the upcoming by-election, which was triggered by incumbent MP Tracy Brabin being elected as West Yorkshire's first metro mayor.
The senior Conservative visited Batley today and said there would be news "very soon" on who the Tories would choose as their candidate in a bid to overturn Ms Brabin's 3,500 majority from the 2019 General Election.
Earlier this week Ms Leadbeater, whose sister Jo Cox was Labour MP for Batley and Spen until she was murdered in June 2016, announced that she would be putting herself forward to be the Labour candidate for the by-election.The 45-year-old said in a statement that she would be "honoured" to "give the people of Batley and Spen the opportunity to put their trust in me" in the election expected to take place this summer.
Mrs Milling told The Yorkshire Post: "What happened to Jo Cox was truly heartbreaking and I remember hearing the news when I was in Parliament. I was so, so shocked, it really demonstrates how we need to kind of come together to tackle divisive views.
"If Kim is chosen by the Labour Party I will wish her the best of luck but we will run a campaign based on what a Conservative MP can deliver for the people of Batley and Spen.
"It's really about the people's priorities and having a really strong voice for the people of Batley and Spen in Parliament."
Recent analysis suggests the number of local elections votes cast in the constituency were evenly split between Labour and the Conservatives. And some bookmakers have made the Tories a strong favourite to win the seat for the first time since 1992.
If Batley and Spen does change hands it will be another blow to Labour leader Sir Keir Starner, who is under pressure after a poor result in the Hartlepool by-election saw it taken by the Conservatives for the first time in decades.
But Mrs Milling said: "This is going to be a very tough battle for us. You look at this seat and it's been in Labour hands since 1997 and also when you look at local government, Kirklees Council, we've only held it for I think three years and that was a very long time ago.
"It's been in Labour hands or no more control with Labour in charge, so this is very much a Labour seat, so it will be a big challenge for us."
She said there would be news "very soon" about the Conservatives' candidate but did not deny that the party may repeat its decision to choose a non-local hopeful as they did in Hartlepool in the form of North Yorkshire farmer Jill Mortimer.
She said: "Ultimately we want to have the best candidate for the seat to be a strong voice for the people of Batley and Spen.
"It will be down to the association to select their candidate but it's about a candidate who will stand up for the people of Batley and Spen, who will focus on the people's priorities here, be a strong voice for the area but also work with government for them to be able to deliver."
Among those understood to be interested in standing locally include former Dewsbury MP Paula Sherriff, Salma Arif, a Leeds council cabinet member, Kirklees Council leader Shabir Pandor and Labour press officer Dan Howard.
The Yorkshire Post understands that a number of people have expressed an interest in being the Conservative candidate but none have yet made their interest public.
Paul Halloran, who stood for the Heavy Woollen District Independents in the 2019 General Election and received more than 6,000 votes, also appears keen to stand.
And this week ex-Bradford West MP George Galloway announced that his Workers Party GB will be contesting the by-election.