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The San Francisco 49ers recently sent an e-mail to all other teams offering second-year safety Taylor Mays in trade.

Matt Maiocco of CSNBayArea.com writes that there’s talk within the locker room that the Bears made an offer for Mays — and that the 49ers rejected it.

Per Maiocco, Mays declined comment, and the 49ers denied that the Bears made an offer.

If an offer was made by the Bears, the 49ers naturally would have been leery. In 2008, the Bears charged the 49ers with tampering in connection with failed trade talks for linebacker Lance Briggs. The 49ers eventually lost a fifth-round pick, and they were required to flip-flop third-round picks with the Bears because the league concluded that the 49ers approached Briggs’ agent regarding a contract extension at the time the trade talks were occurring.

Then there’s the fact that the brother of 49ers coach Jim Harbaugh is the head coach of the Ravens, and that John Harbaugh and other members of the Ravens organization believe that the Bears should have sent a fourth-round pick to the Ravens after a failed effort to swap first-round picks during the 2011 draft.

“They agreed to [trade] a pick,” John Harbaugh said last month during an appearance on ESPN Chicago’s Waddle & Silvy Show. “They got their guy [Gabe Carimi] on the phone. They recognized he wasn’t getting calls from the team behind them. And then they basically stalled for over a minute, telling us that they had called the trade in. So that was just not honest.

“That’s not OK. It’s not ethical, it’s not right. I personally agree with our owner [Steve Bisciotti] that they should have been held accountable for it. We basically took them at their word, and obviously that was a mistake.”

And so the Ravens likely wouldn’t be inclined to do business with the Bears in the immediate future — and John Harbaugh’s brother, Jim, likely wouldn’t be inclined to do business with the Bears, either. Along with the rest of the 49ers organization.