Capito, 59, is considered a moderate House Republican, while Rockefeller, 75, is considered among the Senate's liberal Democrats.
Rockefeller said Capito called him last week to tell him she planned to run.
Earlier this month, a Rockefeller representative said "let there be no doubt that he intends to ask West Virginians for their continued support when the time comes," but Rockefeller has yet to make explicit whether he will run or not.
The senator said Sunday he had other things on his mind. Rockefeller said his "total focus" is on the budget situation in Congress.
"Beyond that big question, every one I talk to in West Virginia is tired of the nonstop campaigning," Rockefeller said Sunday evening. "West Virginians just want us to do our jobs and, for me, that means focusing full time on the serious issues at hand. Politics can wait."
The relationship between Rockefeller and Capito's family goes back.
Her father, former Gov. Arch Moore, beat then-Secretary of State Rockefeller in the 1972 gubernatorial election. The loss has been attributed partially to Rockefeller's opposition to strip mining, an anti-industry position he later abandoned. Moore had to sit out the 1976 race, which Rockefeller won. Then Moore lost to Rockefeller's reelection campaign in 1980.
Capito entered elected life in 1996. She represented Kanawha County in the state House for two terms before running for Congress.
As of mid-October, Capito's campaign had $1.4 million in cash on hand. Rockefeller, by contrast, has not run for office since 2008 and has $700,000.
Capito's exit from the 2nd will likely create a political domino effect in coming months.
Capito fought several tough races in her early years - she was outspent by more than $5 million in 2000. But she faced poorly funded Democratic opponents in both 2010 and 2012. Those un-competitive races allowed the congresswoman to raise and save money she can now use to run for Senate.
Capito's Democratic opponent this year, Howard Swint, spent only several thousand dollars to oppose her - a paltry sum for a modern campaign.
"We certainly had a very productive election year and it gave her the opportunity to better harness resources for the campaign to come," Gates said.
During the past two elections, Capito raised about $3.6 million and spent about $2.2 million. About a fourth of her spending went to the National Republican Congressional Committee to elect Republicans to the House, according to campaign finance filings compiled by the Center for Responsive Politics.
In 2010, Capito won 68 percent of the vote and won every county in her district for the first time. This year, Capito won 70 percent of the vote in her district.