Former Virginia Gov. Tim Kaine said Monday that he is ‘likely’ to seek the seat of retiring Sen. Jim Webb (D), but stopped short of announcing outright that he’s running.

There was buzz on Twitter midday Monday that indicated Kaine, the Democratic National Committee chairman, told a University of Richmond class that he was officially running for Senate. DNC spokesman Brad Woodhouse insisted the student misinterpreted what Kaine said but still indicated that Kaine is closer to running than not running at this point.

“In response to a student’s question, Gov. Kaine told his law school class today what is already widely known which is that he is increasingly likely to run,” Woodhouse said. “However, no final decision will be made or announced until the governor has had a final round of consultations with folks about how he can best serve the president, the people and the causes he cares about; he is assured that the Democratic Party will be in good hands should he choose to make the race and leave the DNC; he has the support that would be necessary to mount a successful campaign and he completes commitments for travel and fundraising he has made to the party and the president through at least the end of the month.”

Kaine’s candidacy would set up what is expected to be one of the most competitive Senate contests in the country next year. If he runs, he is likely to face former Sen. George Allen (R) in the November general election. Allen, who must first win a primary, is attempting to win back the seat that he lost to Webb in 2006.

Roll Call Politics rates the Virginia Senate race as a Tossup.