In search of depth at linebacker and on special teams, the Bears likely would have moved Mays (6-foot-3, 230 pounds) from his customary safety spot to linebacker had the 49ers agreed to the transaction.
But because of the time it would take Mays to make the transition, and with the regular season starting in a little more than three weeks, the Bears backed off.
It was not clear what the Bears were willing to give up for Mays.
According to a report by ESPN NFL insider Adam Schefter on Aug. 4, the 49ers sent out an email to 31 teams informing them that Mays was available in a trade.
A likely scenario would have had the Bears offering the 49ers the 2012 third-round pick they received as compensation from Carolina in the trade involving tight end Greg Olsen.
A second-round pick in 2010, Mays earned first-team All-America honors as a senior at Southern California, but drew criticism from scouts and draft experts coming into the draft for what appeared to be questionable coverage skills.
Mays intercepted just five passes in 50 college starts.
Mays possesses ideal size and speed (sub-4.4 time in the 40-yard dash) but hasn't developed into the playmaker his physical attributes would suggest he is capable of.
What likely appealed to the Bears, however, is Mays could have contributed immediately on special teams while developing as a safety or linebacker.
The Bears have produced one success story -- Brian Urlacher -- in moving a former college safety to linebacker. He made the transition seamlessly as a first-round selection from New Mexico in 2000.
Undrafted rookie Dom DeCicco (6-4, 230 pounds) -- who spent time playing safety at Pittsburgh -- seems to be doing the same, drawing rave reviews from Bears coach Lovie Smith.
Michael C. Wright covers the Bears for ESPNChicago.com and ESPN 1000.