Carter announced on April 30 he would join coach Billy Donovan's team and arrived on campus last month for summer school.
But with the fall semester closing in on Aug. 21, Carter and the Gators still are waiting to see whether he will be eligible to play this season.
Carter, a 6-foot-2 shooting guard who averaged 14.9 points last season, plans to seek a waiver that would allow him to play for UF next season rather than sit out one season under NCAA transfer rules.
Carter has a strong case for a waiver, having left Rutgers after it fired coach Mike Rice for mistreating players.
But on Wednesday, Donovan said Carter has yet to file an appeal with his former school.
“That's really more right now in Rutgers' hands," Donovan said. "He's got to obviously apply for that. He's got to go through writing a letter and then the letter's got to be submitted to Rutgers. Rutgers has got to also submit a letter. But really the people that help in all that is Rutgers, however they want to handle the situation.
"I have not been in contact with them at all. I've really just stayed out of it. It's something that him and his family needs to do."
Carter is not alone. Several former Rutgers players also hope to be eligible to play this season at other schools after each left the program in the wake of Rice's high-profile firing for abusing his players.
"I know a lot of those guys are looking for the opportunity to play right away," Donovan said. "Whether or not that happens, I really don't personally have a feel. All that Eli can do is make an appeal.”
Donovan said he does not have a timeline for when a decision will be made.
"There's a process that he has to go through, and I think what ends up happening is the NCAA gives these guys some guidelines," he said. "There's some things that they've got to talk about in the letter. And then Rutgers has got to handle it as well.
"And because there's different players probably applying for this kind of waiver, I'm assuming Rutgers is going to handle it collectively as one group so to speak when they deal with the NCAA. But I have not heard anything either way in terms of him being denied or actually say that this is going to happen and this is going to work out and he's going to be able to play."
In the end, it would seem Carter would be eligible, given the circumstances behind his decision to leave Rutgers. But Donovan said he would not be shocked if Carter cannot play until 2014-15.
"For me to sit there and pass judgment and say, 'This would be ridiculous if it didn't happen,' I'm just not going to do that because I don't know the ins and outs other than what's been reported on the things that happened there," Donovan said. "I don't know if this is something that the NCAA now goes in on. So they talk to these kids? Does Eli Carter get interviewed? Do they have to speak to him?
"I don't know all the things other than the fact that he has to make an appeal to try to get this waiver."