AP Photo/Thomas Kienzle
A person familiar with the vetting process told the Times that retired Adm. James G. Stavridis, who previously served as NATO's supreme allied commander, was being considered for the position.
The news was confirmed by MSNBC host Andrea Mitchell.
Others rumored to be on Clinton's short list include Sens. Elizabeth Warren and Tim Kaine.
Over the weekend, Republican presidential candidate Donald Trump was reported to be seriously considering retired Lt. General Michael Flynn to serve as his running mate.
Flynn told Business Insider in a Monday interview that it was an "honor" to be among those in the conversation.