But the two lesser-known Republican candidates already in the race say they aren't worried about being big footed.
"I am the Republican front-runner in this race for the nomination and I intend to stay that way," said Howie Lind, a former Navy officer who announced his candidacy for Warner's seat in June.
"It's not a D.C. election, it's a statewide election," Lind told ABC News on Monday. "We have been all over the state for several months."
Shak Hill, a little known Virginia businessman who has also put his hat in the ring, suggested that a Gillespie candidacy could strike just the wrong tone among voters in the state.
"I think the voters are looking more for real community leaders as opposed to 'the politician,' or 'the political insider,'" Hill told ABC News, referencing Gillespie's resume as a top political operative.
So far, Gillespie is just one of a string of rumored 2014 candidacies to have emerged in Virginia as the GOP searches for a candidate with the political muscle to take on Warner.
This weekend, Virginia Attorney General Ken Cuccinelli essentially took himself out of the race after rumors swirled that he might challenge Warner after losing the gubernatorial race in November.
"I don't mind not having an elected role in about a month or so," he told Republicans this weekend, according to reports.
At that same event, both Hill and Lind spoke to Gillespie about his potential candidacy, and Lind said he hopes Gillespie will make his intentions known soon. The state's filing deadline is in March and the primary is scheduled for June. But any candidate will need plenty of time to raise enough money for a successful campaign against an incumbent.
In a statement, Gillespie confirmed to ABC News that he's mulling a Warner challenge after conversations with "many friends" across the state urging him to run.
"I'm going to take some time to talk with fellow Virginia Republicans about how we best win this pivotal Senate seat and, of course, with my own family, who come ahead of politics," Gillespie said. "I'll let you know what we decide."
His potential candidacy was first reported by Politico during the Republican Party's Advance Gala in Virginia this weekend.
Gillespie is a well-liked operative with close ties to the state. He served (albeit for only six months) as chairman of the Virginia Republican Party before resigning to join President George W. Bush's administration.
If he does run, he would become one in a growing list of former political hands in Virginia trading in their advising roles for a stint as the candidate.
Democrat Terry McAuliffe, a former Democratic National Committee chairman and Clinton fundraiser was elected governor in November and Virginia Senator Tim Kaine, another former DNC chairman, was elected in 2012.
The race isn't considered to be a top contest in 2014, especially if Republicans fail to field a candidate who can compete with Warner's likability, fundraising advantage, and upwards of 60 percent job approval rating, according to a September Quinnipiac poll.
A Gillespie candidacy would certainly be more competitive, but it could make the "Washington establishment" argument against Warner a difficult one to make for Republicans.
The Republican Party of Virginia Chairman Pat Mullins declined to comment on a potential GOP primary in this race, as did Warner's campaign and the Democratic Senatorial Congressional Committee.
If Gillespie does run, however, it could give the GOP a much-needed shot at redemption after a bruising 2013 election for Republicans in the state, in which they lost three top state-wide races to Democratic candidates. The Democratic Attorney General candidate has been declared the winner, but the razor thin contest will be recounted.