Last year, Tim Tebow surprised many by announcing his plans to play baseball. What followed was a series of ups and downs for the former quarterback as he fought to achieve his dream. (1:58)

NEW YORK -- Although Tim Tebow did not receive an invitation to big-league camp, New York Mets general manager Sandy Alderson indicated Thursday that the former NFL quarterback will participate in some of the team's Grapefruit League games on loan from minor-league camp.

"Too frequently for some and not frequently enough for others," Alderson deadpanned when asked about how often Tebow would be present. "He'll be around."

Tim Tebow, who signed a minor-league deal with the Mets in September but didn't get an invitation to the big-league camp, hit .194 in the Arizona Fall League. Mike Ehrmann/Getty Images

Tebow, a former Heisman Trophy winner, likely will break camp in April with a full-season minor-league team. He signed a minor-league deal with the Mets in September and proceeded to hit .194 with three doubles, two RBIs and eight walks while striking out 20 times in 62 at-bats in the Arizona Fall League.

"He was in the Arizona Fall League, but that's the only organized league he's ever participated in beyond high school," Alderson recently noted.

"And we understand he's a little bit older so that the process needs to accelerate at some point. But we still need to be prudent about it and put him in situations where he can succeed and not be viewed as, I was going to say, a circus animal. But that's probably not appropriate."

Alderson indicated there's no compelling reason to have Tebow assigned to major-league camp "except for advertising purposes."

"We knew he'd be overmatched in the Arizona Fall League. We also felt that he needed to play games," Alderson added. "And so, as we look at going into spring training and his first full season, I think the same priorities would hold true -- he needs to play games.

"Under most circumstances that would mean, look, he's in minor-league camp. He's playing games every day. He comes over once in a while. And at the end of camp, he goes to a full-season team. I think that's what we would foresee. Now, things could change based on how he performs or what have you."

Manager Terry Collins has suggested that Tebow would be welcome if he had been assigned to big-league camp for spring training.

"We're in New York. We can handle anybody with a name on his back in our camp," Collins said.

"If they decide to send him to camp, we'll get him better. I can tell you, I certainly hope you will see Tim Tebow in some of our games. ... I think he's a name in Florida. He's a star in Florida. He should be. I think it would be fun to have Tim come over. And certainly one thing about our players, they're athletes. They're fans, too. They would probably like to know how to run a quarterback sneak one day."

Said Alderson: "I think the fact that Terry said he would be welcome is indicative of sort of the impact he's had on the organization from a personal standpoint as much as a professional one. This is someone who already has had a positive influence within the clubhouse among his peers. That's one of the benefits we anticipated. It's nice to know that he's the real deal."