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 MurrayPatricia (Patty) Lynn MurrayCDC director to miss fourth hearing because of potential ethics issues Week ahead: Lawmakers near deal on children's health funding Ryan suggests room for bipartisanship on ObamaCare 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 Jean KlobucharOvernight Cybersecurity: Bipartisan bill aims to deter election interference | Russian hackers target Senate | House Intel panel subpoenas Bannon | DHS giving 'active defense' cyber tools to private sector Pawlenty opts out of Senate run in Minnesota Nielsen says 'possible' Trump used vulgar language in meeting MORE (Minn.), Kirsten GillibrandKirsten Elizabeth GillibrandTrump thinks he could easily beat Sanders in 2020 match-up: report Listen: EMILY’s List upbeat about Dem House in '19 Desperate Democrats shouldn't settle for Oprah MORE (N.Y.) and Sheldon WhitehouseSheldon WhitehouseSenate Finance Dems want more transparency on trade from Trump Trump, Kushner meet with advocates on prison reform Democrats search for Russians — any Russians — for collusion story MORE (R.I.) have also been floated as options for the position, but a spokeswoman for Gillibrand said the senator isn't interested.