Another senator, Cory Booker of New Jersey, along with agriculture secretary Tom Vilsack were also among the final contenders, with Mr Kaine having an edge, a Democratic source with knowledge of the discussions said.
Ms Clinton’s campaign declined to comment. She was expected to announce her running mate for the November 8 election through a text message or Twitter.
She will be formally nominated as the party’s presidential candidate at next week’s Democratic convention in Philadelphia. She leads Trump in many opinion polls.
The former secretary of state and first lady’s choice of a running mate would provide a signal about her plan of battle against Mr Trump and help give her campaign momentum as the fight for the White House enters a key stage.
Picking either Mr Kaine or Mr Vilsack, veteran mainstays of the Democratic establishment with plenty of governing experience, would emphasise Ms Clinton’s message that Democrats will offer a serious, steady, alternative to the unpredictable Mr Trump after the chaotic Republican convention.
Mr Booker, a charismatic rising star in the party, could give her candidacy a jolt of energy as Ms Clinton enters the three-month grind of the general election.
Mr Booker, 47, would be the first black vice president and could help boost turnout among young and African-American voters.
Other potential contenders on Ms Clinton’s short list included US senator Elizabeth Warren of Massachusetts, a liberal favourite, Colorado governor John Hickenlooper, and Hispanic cabinet members Julian Castro and Thomas Perez.
Mr Kaine, 58, is a fluent Spanish speaker, having served as a missionary in Honduras. Before entering the Senate, he had been the mayor of Richmond, governor of Virginia, and chairman of the Democratic National Committee.
His presence on the ticket could help Ms Clinton in Virginia, a heavily contested swing state.
Ms Clinton has struggled to unify Democrats and win over liberal backers of her Democratic primary rival Bernie Sanders, a US senator from Vermont. A choice of Mr Kaine would not help that effort.
Liberal groups have pressured her to avoid Mr Kaine, who backs the Pacific free-trade deal known as the Trans-Pacific Partnership. Critics of the deal, including Mr Trump and Mr Sanders, say it would be unfair to US workers and lose jobs.
Mr Clinton praised the deal when she was secretary of state, but now opposes it.
"The best way I can sum up what I hope this election will lead to...is: Love trumps hate." —Hillary— Hillary Clinton (@HillaryClinton) July 22, 2016