In an appearance on CBS's "Face the Nation" program, Specter, who last week switched from the Republican to the Democratic Party, said he would like to see more diversity on the nation's highest court.
"We need more people to express a woman's point of view or a minority point of view," said Specter, D-Pa.
Given that all of the current justices come from federal appellate courts, Specter also said he would like to see Obama nominate a justice who "has done something more than wear a black robe for most of their lives."
Souter, who is generally considered a liberal on the court, plans to leave the bench in June.
On his defection from the Republican Party, Specter said he is becoming increasingly comfortable with the Democratic caucus.
"I was sorry to disappoint many people," Specter said. "Frankly, I was disappointed that the Republican Party didn't want me as their candidate. But as a matter of principle, I'm becoming much more comfortable with the Democrats' approach."