Ken Rosenthal of The Athletic reported the New York Mets are among the clubs trying to sign Bauer, but they're concerned doing so would "renew questions about the team's culture" after general manager Jared Porter was fired after text messages were revealed showing sexual harassment of a female reporter.
Bauer, who's been accused of using social media to harass others but not in a sexual manner, provided a response to those claims:
"I have always tried to be an open book and appreciate that social media gives me a platform to have an open dialogue with fans and the greater public.
"I don't shy away from confrontation and am often quick to defend myself, but I am by no means a bully and I take great offense to my character being called into question. I understand what comes with having a following on social media but I have never asked for nor do I condone anyone making threats or lewd comments on my behalf."
Kate Feldman of the New York Daily News posted a response to Rosenthal's article, saying she was subject to months of harassment after an August exchange on Twitter where Bauer wasn't happy she questioned his COVID-19 viewpoint.
"I had death threats and Holocaust jokes in my mentions for months after he went after me," Feldman wrote. "I didn't tag him. I didn't even [quote tweet] him. This is what his followers did after he told them to go after me. This is OK with his agent, reporters and, I guess, the Mets."
Rosenthal added there was at least one other interaction that led the pitcher's supporters to attack another individual on the social media platform.
The Mets, whom The Athletic report noted have become "more focused" on Bauer in recent days, didn't comment on their interest or the allegations against the star pitcher.
Bauer, 30, was named the 2020 NL Cy Young Award winner for the Cincinnati Reds after posting a 1.73 ERA with 100 strikeouts in 73 innings across 11 starts.