Amid reports that President Obama will nominate former Nebraska senator Chuck Hagel (R) to be his next secretary of defense, Senate Minority Leader Mitch McConnell (R-Ky.) said Sunday that Hagel's record should be given a fair shake in the Senate if he's nominated, but stopped short of saying whether he was prepared to support or oppose his former colleague.

"He's certainly been outspoken in foreign policy and defense over the years," McConnell said on ABC's "This Week With George Stephanopoulos." "The question we'll be answering if he's the nominee is do his views make sense for that particular job. I think he ought to be given a fair hearing, like any other nominee, and he will be."

Another Senate Republican said it was very unlikely that he would vote to confirm Hagel, citing the former senator's remarks about Iran and Israel.

"If Hagel is nominated, it is very difficult to imagine a circumstance in which I could support his nomination," Sen. Ted Cruz (R-Tex.) said on "Fox News Sunday."

Over the past few weeks, Hagel has run into criticism on several fronts as his name surfaced as a leading contender for the job.

His 1998 remarks opposing the nomination of a gay philanthropist for a U.S. ambassadorship prompted pushback from gay rights activists. Hagel has since retracted the remarks, a decision which appeared to assuage concerns of the nation's largest gay rights group.

Hagel has also run into opposition from some Senate Republicans who have warned that he could be in for a difficult confirmation process. The former senator's opposition to  elements of the Iraq War and sanctions against Iran, among other things, stoked GOP concerns.

Obama praised Hagel in a recent NBC News interview, calling him "a patriot." On Sunday, Sen. Heidi Heitkamp (D-N.D.) also lauded Hagel's service and said he should have a chance to present his case in the Senate.

"Chuck Hagel is a tremendous patriot and statesman, served incredibly in Vietnam, served this country as a United States senator," Heitkamp told Stephanopoulos, adding, "let Chuck Hagel get nominated, if he's going to be nominated, and let's hear what the senator has to say."