Story highlights Sen. John Cornyn is on the short list to be the next FBI director

Some of his Republican Senate colleagues want someone else

(CNN) Influential Senate Republicans are questioning whether one of their own -- Senate Majority Whip John Cornyn -- should be tapped to run the FBI, amid a deeply chaotic political environment after President Donald Trump fired James Comey as director of the bureau.

While Cornyn is one of the more popular members of the Senate GOP Conference, a number of his colleagues are skeptical that he would be the right choice for the job, worried that such a pick would be viewed as too political at a time when many critics are questioning whether Comey was fired to slow-walk the FBI's investigation into alleged Russian coordination with the Trump campaign during last year's elections.

On Sunday, Senate Majority Leader Mitch McConnell declined to put his weight behind his top deputy, instead pushing another potential candidate, Merrick Garland , who was former President Barack Obama's Supreme Court pick before the majority leader led an effort to scuttle his nomination last year. Sen. Lindsey Graham, who serves on the Senate judiciary committee with Cornyn, suggested that it made sense to name an FBI agent to the post -- rather than the Texas Republican.

And on Monday, Sen. Susan Collins, who sits on the intelligence committee with Cornyn, said it made sense to choose either Garland or Mike Rogers, a former House intelligence committee chairman and FBI special agent.

"I think the world of John Cornyn, and he would be a great choice in normal times, but we're not living in normal times," Sen. Susan Collins, a Maine Republican, told CNN Monday.

Read More