Democratic National Committee Chairman and former Virginia Gov. Tim KaineTimothy Michael KaineBooker tries to find the right lane  Democrats scramble to contain Franken fallout  GOP campaign committees call on Democrats to return Franken donations MORE is considering a run for the Senate.

Kaine told the Richmond Times-Dispatch he would meet with President Obama in the next few days, perhaps as early as Tuesday, to discuss the possibility of Kaine running for the Senate seat currently occupied by Sen. Jim Webb (D-Va.). Webb recently announced he would retire from the Senate at the end of 2012.

According to the published report, Kaine was "flattered" by Democratic encouragement to seek Webb’s seat, but said he would still need to think about it.

Kaine had previously said he would not run for Webb’s seat if the senator retired in 2012.

Obama picked Kaine in 2009 to run the Democratic National Committee. Kaine served as Virginia’s governor from 2006 to 2010.

Republican and former Virginia Sen. George Allen has already announced his candidacy for Webb's seat. Allen, who made an unsuccessful bid for the Republican presidential nomination in 2008, is expected to face a primary challenge.

Republicans are pushing hard to gain control of the Senate, as are Democrats to retain control. The GOP currently holds 47 seats. The Democrats count 51 senators and two Independents who caucus with the Democrats.