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Donald Trump met Thursday with senators whom he might pick as his running mate

Ohio's Rob Portman, Alabama's Jeff Sessions, and South Dakota's John Thune were among the attendees

CNN —  

Donald Trump sat down with Majority Leader Mitch McConnell and a group of GOP Senate leaders in Washington on Thursday – meetings that included Ohio’s Rob Portman, Alabama’s Jeff Sessions, and South Dakota’s John Thune – all of whom have been mentioned as potential Trump running mates.

A two-term senator from Ohio, Portman is seen as a broadly acceptable figure who would bring legislative experience to a potential ticket. He is also popular in a crucial battleground state, which will be key in November but where Trump lost to John Kasich in the primary.

Portman, however, has been adamant in his lack of interest in the vice presidential nomination. When asked Thursday if he would accept a VP offer Portman told The Hill, “No I’m fine. I’m running for Senate in Ohio,” although he said the meeting “was a good listening session … on both sides.”

Portman is facing a tough re-election fight against former Ohio Gov. Ted Strickland.

RELATED: Trump, Ryan tout unity in wake of meeting

Thune was rumored to be in the running for VP in 2008 and 2012 as well, and offers charisma and legislative experience to balance Trump’s brash style and business background. Thune’s spokesman, however, told the Rapid City Journal earlier Thursday in a statement that the VP role is “not something Sen. Thune is even considering.”

Sessions was the first senator to back Trump and has been the presumptive nominee’s liaison to the Senate. While Sessions would bring loyalty and an insider’s knowledge of Washington to the ticket, he represents a state that is extremely likely to go Republican in the fall. He told CNN in May that it would be “an honor” to be picked as VP, but that Trump has not talked to him about it yet.

Trump told Fox News’ Greta Van Susteren on Wednesday night that at least one woman is on his VP list, and that he would “most likely” choose someone with government experience.