Sen. Patrick LeahyPatrick Joseph LeahyFBI has no excuse to hide future scandals from American public Live coverage: FBI chief, Justice IG testify on critical report Student rips DeVos at school safety commission for failure to take on guns MORE (D-Vt.), the chairman of the Senate Judiciary Committee, said Tuesday that he espouses the view that President Obama should at least consider (if not select) a woman for the Supreme Court.

Obama is considering who he will nominate to replace retiring Justice David Souter.

"I do believe, as many do," Leahy said on MSNBC, "that with nine members of the Supreme Court and only one is a woman...certainly he should consider a woman" for one of those posts.

Leahy, along with Senate Judiciary ranking member Jeff Sessions, Senate Majority Leader Harry Reid (D-Nev.) and Senate Minority Leader Mitch McConnell (R-Ky.), met with Obama Tuesday morning to discuss scheduling the roll out of the nominee and the confirmation hearings that will follow. Obama has said he wants the nominee to be confirmed by the beginning of the Supreme Court's next session in October.

Leahy also said that he and others have "passed on names" of possible jurists to the president. He would not say who he has recommended, however.

But speaking about the possibility of Obama's choice being a woman, Leahy said: "I would be delighted if it is."