Sugano, who arrived in the United States last week in advance of potentially signing with a big league team before the Jan. 7 deadline, had been linked to the Mets as well as the Boston Red Sox, San Francisco Giants, and others.
In December, Sherman cited one non-Mets executive saying they had "as good a chance as anyone" to land Sugano.
Sugano, 31, was posted by the Yomiuri Giants of the NPB on Dec. 7.
He has been elite in Japan, with a career ERA of 2.34 and a 1.03 WHP in eight seasons.
Most scouts believe Sugano -- who features a low-90s fastball, plus slider, and elite command -- profiles as a mid-rotation starter in the majors, with the ceiling of a No. 2 starter.
According to multiple reports, Sugano has a four-year deal (with three opt-outs) on the table from Yomiuri, but the expectation remains that he will sign with a big league club.
As far as the Mets are concerned, with them reportedly out on Sugano, there are a number of free agent and trade possibilities for them to ponder.
Those include Jake Odorizzi, who SNY's Andy Martino has reported the Mets have interest in. Odorizzi has experience working with Mets pitching coach Jeremy Hefner (who worked as an assistant pitching coach with the Minnesota Twins).
Other free agent options include Masahiro Tanaka (though he could possibly return to Japan) and Trevor Bauer. Bauer is reportedly seeking to be paid as much as $40 million annually.
When it comes to the trade market, potential options include Cincinnati Reds RHP Sonny Gray and Cleveland Indians RHP Carlos Carrasco.
No matter where the Mets turn for rotation help, they remain in dire need of at least one reliable pitcher to bolster a rotation that so far only includes Jacob deGrom, Marcus Stroman, and David Peterson.