Kelly said at the NFL meetings in Boca Raton, Fla., on Wednesday that he has talked with Kaepernick but is leaving the personnel decisions to general manager Trent Baalke and Kaepernick's agents.
"Have I done any selling? No. It's just been talking to him, and I don't think there's a selling part," Kelly said. "No. 1, I can't talk offensively with him and say, 'I think this is a good fit because of this, this and this' because you're not allowed to do that. But I did make him understand that just because there is a business side, it doesn't mean that we don't want you here.
"We want him. I really would love to work with him, so I think he understands that."
Baalke said Tuesday the team has had discussions about trading Kaepernick but haven't come close to completing a deal.
According to the Bleacher Report, 49ers owner Jed York has given Kelly the final say on whether Kaepernick remains with the team or is traded.
If Kaepernick is on San Francisco's roster on April 1, a clause kicks in that guarantees $11.9 million of his 2016 contract.