Bennet turned down Reid’s offer in 2010, having just completed a tough race and with Democrats facing an uphill battle to retain the majority in 2012.

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The freshman senator would be taking over a position held by Sen. Patty MurrayPatty MurrayOvernight Healthcare: Takeaways from Price's hearing | Trump scrambles GOP health plans Five takeaways from Price's confirmation hearing Live coverage: Tom Price's confirmation hearing MORE (D-Wash.), who oversaw unexpected gains for Democrats this year when the party added two seats.

Democrats again will have a challenge holding onto the Senate going into the 2014 elections, as six of their party members will be running in red states and six will compete in swing states.

But Bennet's experience running in a swing state, as well as his ability to relate well to colleagues, could be an asset to the committee, sources say, as Democrats plan to place a large emphasis on recruitment, which boosted their efforts this past Election Day.

Sens. Amy KlobucharAmy KlobucharTrump could mean new momentum for drug imports Sanders to roll out bill letting Medicare negotiate drug prices WHIP LIST: How many Dems will back Sessions? MORE (Minn.), Kirsten GillibrandKirsten GillibrandOvernight Defense: Obama defends Manning commutation after backlash | Mattis clears Senate panel Senate panel approves Mattis for Defense secretary Overnight Finance: Price puts stock trading law in spotlight | Lingering questions on Trump biz plan | Sanders, Education pick tangle over college costs MORE (N.Y.) and Sheldon WhitehouseSheldon WhitehouseFive takeaways from Pruitt's EPA hearing Health pick’s trades put STOCK Act in spotlight Dems prepare to face off with Trump's pick to lead EPA MORE (R.I.) have also been floated as options for the position, but a spokeswoman for Gillibrand said the senator isn't interested.