Grimes, who has played five NFL seasons, all with the Falcons, is looking for a long-term deal, though the team has not obliged. Instead Atlanta placed the franchise tag on him.
Grimes went undrafted in 2007 and has worked his way up to starter. He went to the Pro Bowl as an alternate following a 2010 season in which he had five interceptions. Last year, in 12 games, Grimes had one interception and one forced fumble.
Dimitroff has previously said the team planned to continue discussions and wasn't opposed to striking a long-term deal.