Iowa Gov. Terry Branstad (R) will hold a news conference at the State Capitol Tuesday afternoon on the Republican presidential race.

Branstad, who has not yet thrown his weight behind a contender, hinted late last week that he might give an endorsement soon.

 “We’ve had a very good, open contest, and I respect and appreciate Senator [Rick] Santorum and all the other candidates, as well,” he told Iowa reporters on Thursday. “But I think we’re getting close to the point where Republicans need to unite. We cannot afford to continue the direction this country is going. We need new leadership.” 

That would suggest that Branstad might be considering GOP frontrunner Mitt Romney. Neither Romney’s nor Branstad’s office immediately responded to requests for comment. 

The ties between Romney and Branstad stretch back to 2010, when the former Massachusetts governor backed Branstad in Iowa’s tough GOP gubernatorial primary. Some other influential Republicans, including former Arkansas governor Mike Huckabee, endorsed Branstad’s opponent, Bob Vander Plaats, in the race. 

At the staff level, Branstad and Romney also have some top operatives in common: Branstad’s communications director, Tim Albrecht, served as top Iowa press aide to Romney in 2008. And Doug Gross, a top Branstad backer, was chairman of Romney’s Iowa effort four years ago.

Tuesday’s event, set for 1:30 p.m. Eastern and to be live-streamed on the governor’s Web site, comes as Romney is rounding up endorsements from top Republicans including President George H.W. Bush, Sen. Marco Rubio of Florida and House Budget Committee Chairman Paul Ryan of Wisconsin.