Former Virginia Gov. Tim Kaine will not announce whether he’ll run in 2012 for Jim Webb’s Senate seat at the Jefferson-Jackson dinner Saturday, a DNC official has confirmed.

Democratic officials have been pushing Kaine to get into the race, and Kaine, now chairman of the Democratic National Committee, discussed the matter with President Obama Wednesday. But the timeline for an announcement on the race will be later in the month or early next month, the official said.