In an interview with Yahoo Sports, Hudson said he can't understand why Dye, a free agent who hit 164 home runs for the Chicago White Sox from 2004 through last season, did not catch on with another team in the offseason.
"You see guys like Jermaine Dye without a job," Hudson told Yahoo. "Guy with [good numbers] and can't get a job. Pretty much sums it up right there, no? You've got some guys who miss a year who can come back and get $5 [million], $6 million, and a guy like Jermaine Dye can't get a job. A guy like Gary Sheffield, a first-ballot Hall of Famer, can't get a job."
"We both know what it is. You'll get it right. You'll figure it out. I'm not gonna say it because then I'll be in [trouble]," Hudson said.
Dye and his agent, Bob Bry, declined to comment, Yahoo said.
The 36-year-old Dye, who has a career. 274 batting average and 325 home runs in 14 major league seasons, reportedly turned down the Washington Nationals and Chicago Cubs before the season. The teams' offers reportedly were significantly lower than the $11.5 million Dye made in the final year of his White Sox contract.
Dye hit 27 homers and drove in 81 runs last season, but Chicago did not re-sign him after he slumped badly following the All-Star break.
Still, Hudson said Dye's consistent production at the plate in the last several years warranted him getting a stronger look in free agency.
"There are some things that go on in the game that shouldn't be going on," Hudson told Yahoo. "But it's part of baseball. It's part of life. Deal with it."
"Call it what you want to," he added. "I ain't fit to say it. After I retire I'll say it. I've got a whole bunch of stuff to say after I retire."
Seattle station KIRO reported Tuesday that Dye has interest in playing for the Mariners.
"Seattle is a team he focused on this offseason," Bry told the station. "He was disappointed that there was not more interest from the club."