CINCINNATI -- A reunion of the Reds and free agent starting pitcher Bronson Arroyo remains a possibility, and a decision could be coming soon. But there are other teams in the mix that also have expressed interest.

Arroyo told MLB.com on Monday that he threw a bullpen session in Cincinnati on Friday with Reds catching coach Mike Stefanski. No one from the Reds' front office was present, but the session was put on video for the club to watch.

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"I told them I'm healthy, but they want to see it with their own eyes," Arroyo said. "I hope the Reds make a bid at me today."

A source told MLB.com that the Reds would have interest in bringing Arroyo back if the price was right for the club. He missed the entire 2015 season while rehabilitating from Tommy John surgery on his right elbow.

The right price is also on the mind of Arroyo, who expects to sign an incentive-laden contract anywhere he goes. He has a Minor League offer already from the Nationals, which would bring him and former Reds manager Dusty Baker back together.

"I wanted to give the Reds every opportunity to keep me," Arroyo said. "[Manager] Bryan Price has told me he'd love to have me in their locker room.

"I think it benefits both sides. It's an opportunity for me to come into a less-stressed situation after a surgery and help young guys on the staff. If we can get something that's in the ballpark [financially], I'd be happy."

Reds medical director Dr. Tim Kremchek examined Arroyo's arm last week. He underwent X-rays and had his elbow checked.

"My arm feels fine, totally normal," Arroyo said. "It took 16 months to feel this way. The only question mark in my mind is endurance. How long can I go? I'd be lying if I said I knew I could throw 200 innings with this arm. I just don't know."

Arroyo's girlfriend lives in Cincinnati, and he frequently visits the city. When he's in town, he's been allowed to work out and throw at Great American Ball Park. He was headed to the ballpark Monday afternoon for a lifting session.

Arroyo, who will turn 39 on Feb. 24, feels the Reds would be a good fit for him because of his familiarity with the city, staff and team facilities. He pitched in Cincinnati from 2006-13 and was 105-94 with a 4.05 ERA in 265 starts over his eight seasons. He never missed a start during that time because of injury.

With the Reds' rotation currently counting Homer Bailey as its only veteran, Arroyo would be an added mentor for the team's many young and inexperienced pitchers. Bailey is also trying to come back from Tommy John surgery and won't be ready until May at the earliest.

The Marlins, Pirates and Padres have also expressed interest in Arroyo but have not made any serious overtures as of yet.

"There is more of a need here [in Cincinnati] for my mind in this locker room than just basic pitching," Arroyo said. "Other places might take my mind and what I have to offer but would need my physical ability more."