"We're very sensitive to it, and we're monitoring it and we're still, as [general manager Ozzie Newsome] says, we're scrimmaging it," Bisciotti said at a fan forum with NFL commissioner Roger Goodell at M&T Bank Stadium. "We're trying to figure what's the right tact. Pray for us."
Kaepernick has been a free agent since March 1 when he opted out of his contract with the San Francisco 49ers. He drew national attention last season when he knelt during the national anthem before games to protest social injustice, which he said he will no longer do in 2017.
Ravens officials said they've spoken with Kaepernick and he is committed to playing football. The Ravens have talked about the possibility of adding Kaepernick with current players, former players including Ray Lewis, fans and sponsors.
Ravens coach John Harbaugh first brought up Kaepernick last week after he said Joe Flacco would miss a week with a back injury. Backup Ryan Mallett has since struggled while filling in with the first-team offense, throwing at least five interceptions one practice.
Bisciotti said there are also football factors to consider with Kaepernick.
"We do want to win games, and I'm not sure he is going to help us do that," Bisciotti said. "We're monitoring Joe [Flacco and his back injury]. We've talked to Joe about it. We're monitoring [backup Ryan] Mallett and keeping our door open. We've talked about RG3 [Robert Griffin III] and bringing him in for a workout."
NFL commissioner Roger Goodell was asked whether he would like Kaepernick to get another chance in the league.
"Those are football decisions that each team has to make. What they think are the right ways to make their football teams better," said Goodell, who shot down the notion that Kaepernick has been blackballed. "Those are decisions I don't get involved with, decisions that rightfully belong with the club."
Linebacker Terrell Suggs, the Ravens' longest-tenured player on the roster, said he would be accepting of Kaepernick if he was signed by the team.
"Hell yeah, if he's going to help us win," Suggs told ESPN on Sunday night. "We have no issues. Not in the locker room. Hell yeah, we want him."