Sen. Lindsey Graham, R-S.C., said he would further investigate the Hillary Clinton email controversy should he become chairman of the Judiciary Committee next year.

Asked by CNN about whether he would pursue answers on the FBI-run emails inquiry as well as another FBI investigation into Russian interference in the 2016 election, Graham said "totally."

"The oversight function will be very much front and center," he added.

Graham's rise to the chairmanship of the Judiciary Committee isn't a sure thing; that will largely depend on whether current Chairman Chuck Grassley, R-Iowa, will seek the top spot over in the Finance Committee.

Graham also told CNN he would support any bill to protect special counsel Robert Mueller if one came to the floor, even though, he added, "I don't see any threat to Mueller."