Kansas City, Mo. ? With salary-cap space to spare after losing tackle John Tait to free agency and missing out on cornerback Troy Vincent, the Chiefs are looking into Tampa Bay’s Warren Sapp.

Pursuit of the Tampa Bay Buccaneers’ flamboyant defensive tackle happened after a call from Sapp’s agent, Drew Rosenhaus, to Chiefs head coach Dick Vermeil. No visit was scheduled.

Rosenhaus said Thursday it was unlikely Sapp would be in Tampa next season and there was a “mutual interest” between the Chiefs and the seven-time Pro Bowler. Sapp has a similar interest with Cincinnati, Rosenhaus said.

The Bucs have signed a number of players in the past week, but ignored the Super Bowl champ, who has played his entire nine-year NFL career in Tampa.

Since the Chiefs had about $9 million of cap room before the recent signings of offensive lineman Chris Bober and tight end Jason Dunn — and because they need a skilled defensive tackle — the possibility of Sapp joining Kansas City can’t be dismissed.

But Vermeil wasn’t optimistic.

“Right now, this is all talk,” he said. “I don’t think it will materialize.

“We probably don’t have the money to sign him (Sapp),” Vermeil said. “If he’s going to the highest bidder, he’s probably going somewhere else. But sometimes they don’t go to the highest bidder because they want to play for a winner.”

Tampa Bay's Warren Sapp, right, sacks Dallas quarterback Quincy Carter in this file photo. The Kansas City Chiefs are looking into signing Sapp to shore up their shoddy defense.

Even though the Chiefs have the available cap space to sign Sapp, they dished out more than $16 million in bonuses to players like running back Priest Holmes, quarterback Trent Green and others this winter.

Vermeil said those payments affected the Chiefs’ offer to Vincent and would guide their efforts with Sapp.

Vermeil also said he hadn’t thoroughly researched Sapp’s potential fit with the Chiefs. Sapp has a reputation for being an attention-seeker with a loud mouth.

“I don’t know if he would completely fit the profile I’m looking for,” Vermeil said. “But I think he could fit with the influence of everybody else.”

The Chiefs could use Sapp, 31, one of the NFL’s best defensive tackles for nine seasons.

His addition would fill the Chiefs’ most immediate personnel need and give them an impressive three-tackle rotation with Ryan Sims and John Browning, who would also then be free to help at defensive end.