The Bears later confirmed the move.
Grant signed a one-year, $755,000 contract with the Bears after they terminated Mark Anderson's contract, but he was inactive for games against the Carolina Panthers and Seattle Seahawks before he was let go by the team.
"I guess the last one in is the first to go," Grant told the Tribune. "I guess they were looking for something different. I appreciate them bringing me in, but I didn't even get a chance to get on the field."
Bears defensive coordinator Rod Marinelli indicated that Grant, who had 47 sacks in eight seasons with the New Orleans Saints, would be used as an outside rusher. But the team seems more interested in developing rookies Corey Wootton and Barry Turner.
"This is a business, and I know the (trade) deadline is today," Grant said. "I'm not knocking them at all. I just don't think I got a fair chance. But it is what it is."
The Bears didn't make a trade by the 4 p.m. ET deadline and called up rookie defensive end Barry Turner from the practice squad to fill Grant's roster spot.
Grant was cut by the Saints in March and also released by the Miami Dolphins before he played two games with Omaha in the United Football League. Grant started 16 games for the Saints last season before an arm injury forced him to miss the playoffs.
The Associated Press contributed to this report.