(CNN)Democrats in Washington and Kentucky, eager to seize on Sen. Rand Paul's stumbles in the Republican presidential race, are increasingly setting their sights on what once seemed unthinkable: Knocking him out of his Senate seat.
The prospects, they acknowledge, are still slim -- given Kentucky's sharp tilt to the right in recent years. But behind the scenes, Democrats are urging the wealthy mayor of Lexington, Jim Gray, to mount a campaign that he could finance partly on his own, arguing he has at least an outside shot of taking out Paul.
Paul and his team are watching Gray closely, and his decision on whether to run -- expected by the state's filing deadline next week -- could impact the Kentucky Republican's calculation on how long to stay in the presidential race.
Gray and his team met this month with Sen. Jon Tester, head of the Democratic Senatorial Campaign Committee, and senior staff to discuss his interest in running. He has spoken with a number of Kentucky Democrats, including the lone Democrat in the congressional delegation, Rep. John Yarmuth. And the advice he's been getting seems to be universal: Run against Paul.
"I think at this point he's our strongest possible candidate, without question," Yarmuth said. "It sounded to me like it was something he really wanted to do."
Tester told CNN: "I think he can absolutely be competitive in Kentucky," adding that Gray is a "very, very appealing" candidate.
Gray and Paul both declined to be interviewed.
Even as he's been focused on his presidential run over the past year, Paul's team is preparing for the likelihood of a Senate reelection bid and leaving nothing to chance, according to several people involved in the discussions. They say that they are still holding out hope Paul pulls off a surprising comeback in the White House race. But they fully acknowledge that running a Senate race could cost well over $10 million, requiring an organization that takes time to build.
