Per MLB Network's Jon Heyman, the San Francisco Giants and Toronto Blue Jays are among the teams hoping to add the 31-year-old.
Heyman added that the New York Mets have talked with Sugano's representatives, but their "main focus is elsewhere."
Sugano has been arguably the best pitcher in Nippon Professional Baseball since making his debut for the Yomiuri Giants in 2013. He has won the Central League MVP award twice, including in 2020 when he finished 14-2 with a 1.97 ERA and 97 hits allowed in 137.1 innings over 20 appearances.
Per MLB.com's J.P. Morosi, Sugano is considered to be the second-best free-agent pitcher available this offseason behind 2020 National League Cy Young winner Trevor Bauer.
"One MLB scout said Monday that Sugano’s fastball has late action and typically ranges from 91-93 mph, topping out at 95," Morosi wrote. "Sugano's slider is known as his best secondary offering, and he also throws a forkball and changeup that can be above-average pitches."
The Yomiuri Giants formally posted Sugano on Dec. 8, giving all 30 MLB teams 30 days to negotiate with his representatives. If he decides to play in MLB, a deal must be completed by 5 p.m. ET on Jan. 7.
ESPN's Jeff Passan reported after Sugano was posted that the Boston Red Sox, San Diego Padres and Texas Rangers were interested.
The Padres have since acquired Blake Snell and Yu Darvish in separate trades with the Tampa Bay Rays and Chicago Cubs. It's unclear how much interest they still have in adding Sugano to their rotation.
The Blue Jays have a young offensive nucleus and are in need of pitching depth to maximize their full potential. Hyun Jin-Ryu was terrific in his first season with the team, posting a 2.69 ERA last season. Taijuan Walker was the only other they had who made at least six starts and posted an ERA under 4.71.
The Giants are stuck between trying to contend and wanting to rebuild after going 29-31 last season. They have missed the playoffs in each of the past four years and haven't finished higher than third in the NL West since 2016.
Sugano is a six-time All-Star in NPB and is a two-time winner of the Eiji Sawamura Award as the league's top pitcher.