Morosi, who described the Blue Jays as being "among the most active MLB teams in off-season talks," noted that adding another lefty to the bullpen is on the team's wish list.
Right now, Toronto has lefty relievers Rafael Dolis (1.50 ERA in 24 innings in 2020) and Jordan Romano (1.23 ERA in 14 2/3 innings) on its roster.
Hand became a free agent last month after the Cleveland Indians declined his $10-million option. The 30-year-old was arguably baseball's best closer in the shortened 2020 season, going 2-1 with a 2.06 ERA and 16 saves in as many chances.
"With Brad it was a really difficult decision," Indians president of baseball operations Chris Antonetti said. "He's been such a critical part of our team for the last few seasons. He did an extraordinary job in his role as a closer and also was a leader in the clubhouse, specifically within the bullpen group.
"In the end, we did take some time to explore the trade market for Brad and weren't able to find a fit for him. Again, a very difficult decision."
Fangraphs predicts Hand to receive a three-year contract valued at $27.9 million.
-- With files from the Associated Press