Among those travelling to Washington, DC, to meet Ms Harris are Governor Josh Shapiro, Senator Mark Kelly and Governor Tim Walz.
The choices for the Democratic vice-president has been narrowed to a group of five, according to CBS, the BBC’s US partner.
A decision is required before the Democratic National Convention, which starts on 19 August in Chicago.
It is unclear whether other potential candidates, including Kentucky Governor Andy Beshear or Transportation Secretary Pete Buttigieg, were scheduled to meet with Ms Harris.
Harris officially became the Democratic presidential nominee on Friday in a vote of party delegates.
Once Ms Harris’s running mate is announced, the two are expected to tour the battleground states.
Mr Shapiro has seen high approval ratings since he was elected in 2022 and could help Ms Harris capture Pennsylvania – a must-win state in the race for the White House.
Arizona Senator Mark Kelly, a former Navy pilot and Nasa astronaut, has become a leading voices on gun safety and his strong border stance and occasional criticisms of the Biden administration could help appeal to independent and conservative voters.
Mr Walz, who served 12 years in Congress before becoming governor of Minnesota in 2019, gained national attention for his strategy calling Donald Trump and JD Vance “weird”.
On Friday President Joe Biden said he had spoken to Ms Harris about her search for a running mate. Asked what qualities she should look for in a vice-presidential candidate, he said: “I’ll let her work that out.”
Potential partners to join Ms Harris on the Democratic ticket for November’s election face an exhaustive vetting process, having to answer up to 200 questions
The United Automobile Workers, a major US union representing more than 400,000 people, said its preferred vice-presidential pick was Mr Beshear, who “stood with us on the picket line and has been there for workers”.
Speaking to CBS’ Face the Nation, UAW President Shawn Fain added that Mr Walz was also “100% behind labour”, but he criticised Mr Shapiro’s support of private school vouchers in Pennsylvania – a Republican-backed proposal to send $100m to families for private school tuition and school supplies.
Meanwhile, Donald Trump’s allies have been forced to defend the former president after he questioned Ms Harris’ racial identity during a heated exchange at a convention for US-based black journalists.
Trump said of Ms Harris: “I didn’t know she was black until a number of years ago when she happened to turn black and now she wants to be known as black. So I don’t know – Is she Indian? Or is she black?”
Ms Harris’ mother was born in India and her father is from Jamaica. She has always identified as both Indian American and black.
Senator Lindsey Graham of South Carolina, a Trump ally, said he would advise the former president to focus on the Biden-Harris administration’s policy decision – not the vice-president’s heritage.
“Every day we’re talking about her heritage and not her terrible, dangerous liberal record throughout her entire political life [is] a good day for her and a bad day for us,” Mr Graham told Fox News Sunday.
Earlier in the day, Senator Laphonza Butler, a Democrat who represents Ms Harris’ home state of California, called the comments about the vice-president’s heritage “despicable” and “an insult” during an appearance on CNN.
“This is a woman who was born in Oakland, California, who has declared and lived proudly all of her identities her entire life, embracing the totality of who she is,” she told CNN.
BBC