According to the report, the Mets are looking to move Harvey for a reliever.
On Sunday, the first night of the annual MLB winter meetings, Mets general manager Sandy Alderson told reporters that no player in the organization is untouchable.
Harvey, who was suspended three games last season after failing to show up for a game in May, is eligible for arbitration this winter and then free agency in the fall of 2018.
Harvey, 28, was 5-7 with a 6.70 ERA in 18 starts last season after returning from surgery for thoracic outlet syndrome that cut his 2016 season short. He made only 17 starts that season, going 4-10 with a 4.86 ERA.
He was an All-Star in 2013 when he went 9-5 with a 2.27 ERA. He also pitched well in 2015, finishing 13-8 with a 2.71 ERA.
Harvey made two starts in the 2015 World Series after missing the 2014 season following Tommy John surgery.