TUESDAY: The Mets “don’t have any real interest” in Lawrie, per MLB.com’s Anthony DiComo (via Twitter). As he notes, New York does have quite a few depth options in the infield, and it seems the team is pleased with the quality on hand to provide protection for the questionable status of David Wright.

As for the Rays, the club wouldn’t be looking to utilize Lawrie at his accustomed positions of third and second, per Marc Topkin of the Tampa Bay Times (Twitter link). Rather than competing for time in those areas, he’d be expected to appear at first base, DH, and perhaps even in the outfield.

Meanwhile, it’s worth wondering whether Toronto’s interest could be impacted by the slow progress being made by Blue Jays second baseman Devon Travis. As Ben Nicholson-Smith of Sportsnet.ca tweets, skipper John Gibbons says the club expected Travis to have advanced further by this point but will continue “to be cautious.”

SUNDAY, 4:10pm: The Royals, Mets and Blue Jays also have interest in Lawrie, according to ESPN’s Jim Bowden. A native of Canada, Lawrie played in Toronto from 2011-14.

12:33pm: The White Sox released Brett Lawrie on Friday, but the infielder might not be without a team for long. The Rays will at least consider signing Lawrie, reports Marc Topkin of the Tampa Bay Times.

Now 27, the version of Lawrie who served as one of baseball’s top prospects before torching opposing pitchers as a rookie with the Blue Jays in 2011 (.293/.373/580 in 171 plate appearances) is long gone. A career .261/.315/.419 hitter in 2,417 lifetime PAs, Lawrie slashed a pedestrian .248/.310/.413 in 384 plate trips last season and failed to provide defensive value at second base (minus-4 Defensive Runs Saved, minus-5.5 Ultimate Zone Rating).

Lawrie has spent his career at both the keystone and third base, where the Rays have far better starting options in Brad Miller and Evan Longoria, but they find his right-handed bat intriguing, according to Topkin. Moreover, because of injuries, infielders Matt Duffy (shortstop) and Logan Morrison (first base) aren’t locks for Opening Day, so Lawrie could provide the club depth if they do end up unavailable. Jason Martinez of MLBTR and Roster Resource projects that Tampa Bay will enter the regular season with two out-of-options players, Nick Franklin and Tim Beckham, and minor league signing Rickie Weeks as its infield-capable bench choices. Like Lawrie, all three bat from the right side (Franklin’s the only switch-hitter of the group).