Senate Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellDems confront Kelly after he calls some immigrants 'lazy' McConnell: 'Whoever gets to 60 wins' on immigration Overnight Defense: Latest on spending fight - House passes stopgap with defense money while Senate nears two-year budget deal | Pentagon planning military parade for Trump | Afghan war will cost B in 2018 MORE (R-Ky.) has been lobbying behind the scenes for a Kentucky bill that would allow a candidate to run for two federal offices at the same time, according to a state senator.

Kentucky Sen. Damon Thayer (R) on Thursday officially introduced a bill aimed at clarifying a state law that would allow U.S. Sen. Rand PaulRandal (Rand) Howard PaulPentagon: War in Afghanistan will cost billion in 2018 Overnight Finance: Senators near two-year budget deal | Trump would 'love to see a shutdown' over immigration | Dow closes nearly 600 points higher after volatile day | Trade deficit at highest level since 2008 | Pawlenty leaving Wall Street group Rand Paul calls for punishment if Congress can't reach a long-term budget deal MORE (R-Ky.) to appear on the ballot for the presidency in 2016 as well as reelection to the Senate. 

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Thayer said he introduced the bill after being approached by Paul’s staff and told the Lexington Herald-Leader that McConnell is “strongly behind” the proposal as well, and has been making calls to state lawmakers about it. 

"I know he's in favor of this, and he's been working behind the scenes to try to help," Thayer told the newspaper about McConnell. 

McConnell has formed an alliance with the junior senator since his election in 2010, and Paul has endorsed McConnell’s reelection bid this year.

Thayer admitted the chances that the proposal would be approved are “quite small.”

Thayer had announced earlier this week he was planning on introducing legislation regarding a state law that says, in part, “no candidate’s name shall appear on any voting machine or absentee ballot more than once.”

Thayer’s bill would clarify that the law would not apply “if one or both of the [offices] sought is a federal office.” 

Paul has made no secret that he is considering a run for the White House in 2016. His advisers have previously told the newspaper that if he did enter the race, the Kentucky law would not hold up to constitutional scrutiny. 

A 1995 Supreme Court decision found that federal law, not state law, governs federal elections, his allies say. 

A spokeswoman for Kentucky Secretary of State Alison Lundergan Grimes, who is running for Senate, said the office would seek guidance from the attorney general and the courts if the current law were tested.  

Taking a jab at Paul, Kentucky House Speaker Greg Stumbo (D) said a candidate who can’t decide which office he wants to hold “isn't fit to hold either.”