Toronto general manager Alex Anthopoulos said that Lawrie, on a rehab assignment with Class-A Dunedin, will play at second base the next few games to see whether it works out.
Lawrie has played most of his career at third base, though he did play some second base when he was coming up through the Milwaukee Brewers' farm system.
"We know he can do it. He's done it before," Anthopoulos said before Sunday's game against Kansas City. "Even if we don't need to do it now, we'll have it in the back pocket that he can."
The move would allow Maicer Izturis to take Reyes' place at shortstop. Jose Bautista would continue at third base, and Rajai Davis and Emilio Bonifacio would split time in right field.
Anthopoulos is also exploring trade options for a shortstop, though he warned that he won't overspend for a stop-gap that can fill in until the Blue Jays' All-Star returns.
Reyes was hurt in the sixth inning of Friday night's series opener when he slid awkwardly into second base. An MRI revealed a significant sprain of his left ankle, and the Blue Jays do not expect Reyes back until the middle of July.
He remained with the team Sunday, hobbling around on crutches with his ankle in a boot.
Munenori Kawasaki was brought up to help out at shortstop on Saturday, and he was starting alongside Izturis at second base on Sunday. Anthopoulos didn't rule out Kawasaki sharing time at shortstop until Reyes returns, but he's hopeful Lawrie is able to create some flexibility.
"When I called him, I said, 'What do you think?'" Anthopoulos said, "and he was very receptive. If I told Brett, 'I need you to pitch two innings,' he'd say, "Sure, I can throw two shutout innings.' He feels very strongly he can do it and be good at it."
Lawrie's appearance at second base Sunday was to be his first game action since sustaining a rib injury March 6 in an exhibition game for Canada ahead of the World Baseball Classic.
He's coming off a season in which he hit .273 with 11 homers and 48 RBIs in 125 games.
Lawrie's move to second would only work if Bautista is willing to take over at third base on a permanent basis. The slugger has played primarily in the outfield the past four seasons, but has appeared in 385 career games at third base.
"Jose's always the same. Wherever the team needs him, he'll do it," Anthopoulos said. "It's a good problem to have when you can play two positions really well."