Caperton served as governor throughout the early '90s and was initially considered a possible contender in what will likely be a tough race for Democrats in 2014. Republicans already have their top recruit for the seat in Rep. Shelley Moore CapitoShelley Moore CapitoLawmakers try again on miners’ pension bill How the effort to replace ObamaCare failed It's time to eliminate the secretive Pharmacy Benefit Manager pricing practices MORE, who is thus far the only candidate to officially announce a bid.

No Democratic front-runner has yet emerged following Rockefeller's announcement on Friday that he will not be running for a sixth term in 2014. A handful of others have indicated interest in the seat, including Democratic Secretary of State Natalie Tennant, state Supreme Court Justice Robin Davis and, reportedly, former West Virginia Democratic Party Chairman Mike Callaghan.

One top Democratic pick, former Sen. Carte Goodwin, who was appointed to finish Sen. Robert Byrd's (D) term after his death in 2010, has not ruled out a bid. But he also hasn't openly expressed interest.

“There will be plenty of time for people to make decisions like that,” Goodwin said when asked about a potential bid. “It’s the kind of thing that anybody would be flattered to have their name contemplated for a position like that.”