The decision is all but done on the Democratic side of the primary. Barring something unprecedented happening, Hillary Clinton will be the Democratic nominee. With that decision out of the way, the Clinton campaign can begin looking at the potential vice presidential picks.
Among the names under discussion by Mrs. Clinton, Mr. Clinton and campaign advisers: Senators Tim Kaine and Mark Warner, former governors from the key state of Virginia; Senator Sherrod Brown of Ohio, who represents both a more liberal wing of the party and a swing state; former Gov. Deval Patrick of Massachusetts, a prominent African-American Democrat; and Thomas E. Perez, President Obama’s labor secretary and a Hispanic civil rights lawyer.
The article also states that Sen. Elizabeth Warren of Massachusetts is also a possibility.
I highly doubt that this is an inclusive list. There are also names on this list that seem less probable running mates than others. Still, it is a good place to start.