Barring a breakdown in contract negotiations, Jackson figures to sign with the Jaguars as early as Tuesday, sources said.
In a surprising move, the Falcons last Tuesday released the 11-year veteran, who had started in 22 of 23 games since signing with the franchise as an unrestricted free agent in 2006 and who has long been regarded as one of the NFL's toughest interior defenders.
Landing Jackson would add further depth and experience to a defensive tackle that already rates among the NFL's best.
The Jaguars feature a pair of Pro Bowl tackles in former first-round draft choices Marcus Stroud and John Henderson. The backups are Rob Meier, Tony McDaniel and Derek Landri. But the Jaguars, who statistically rank No. 15 in the league in both total defense and defense versus the run through the first eight weeks of the season, haven't yet gotten the kind of play at the position to which they are accustomed.
Stroud underwent offseason microfracture surgery to address a chronic ankle problem and his rehabilitation stretched into training camp, where he was limited to one practice per day. Henderson has struggled at times in 2007 to reach his past performance level. There is some suspicion that Henderson is not 100 percent physically.
Grady has the kind of size head coach Jack Del Rio and defensive coordinator Mike Smith prefer upfront, and he would fit well with a unit whose first priority is to stop the run.
Jacksonville is one of several teams to have contacted agent Angelo Wright about Jackson and is the only franchise with which he has scheduled a visit. There have been preliminary contract discussions, and the two sides are expected on Tuesday to ramp up the negotiations, provided the visit goes well.
The day after his release, Jackson said his priority is to sign with a playoff contender.
Last week's abrupt release of Jackson, whose physical presence and ability to command double-team blocking helped improved the Falcons' run defense in 2006, ended a brief but tumultuous relationship between the team and the player.
In March, Jackson, upset over his contract status, sued the Falcons for defamation and invasion of privacy, claiming team officials had leaked information to the media about the physical examination he took with the club in 2006. Jackson charged that the negative information, which suggested he might have a heart condition, scared off other potential suitors who might have considered signing him.
The lawsuit was eventually resolved and the Falcons reworked Jackson's contract, adding a year to the deal he originally signed in 2006 and providing him a mechanism to earn more money. Under the new deal, the Falcons paid Jackson a $250,000 signing bonus and a roster bonus of $250,000, in addition to his $1 million base salary for 2007.
Jackson, 35, was under contract through 2009, at base salaries of $1 million each year, and with roster bonuses of $2 million in the spring of 2008 and 2009.
Falcons coach Bobby Petrino said the release of Jackson was strictly a football decision, and it is true that he was not playing well and was uncharacteristically doing a lot of freelancing and playing outside the directives of the Atlanta scheme. But team sources also conceded that part of the rationale in releasing Jackson was to send a message to some veterans on the slumping team.
His spotty play this season aside, few players can clog the inside like Jackson and, even at his age, he is still effective.
In 146 career games, Jackson has 440 tackles, 33½ sacks, eight forced fumbles, six fumble recoveries and 26 pass deflections.
The former Knoxville College star began his career with the Oakland Raiders and played there for five seasons (1997-2001). He has also had stints with New Orleans (2002-03), Green Bay (2004-05) and the Falcons (2006-07).
Len Pasquarelli is a senior writer for ESPN.com.