Sheffield, a nine-time All-Star who was released Tuesday by the Detroit Tigers, held a private workout Thursday for several teams interested in signing him, including the Mets. Following the workout, the team had been working on determining whether it could find enough at-bats for Sheffield to justify signing him.
The Cincinnati Reds and Philadelphia Phillies also had expressed interest in signing Sheffield.
"It is a good fit for Gary," Sheffield's agent, Rufus Williams, told Andrew Marchand of 1050 ESPN New York. "He has a lot of respect for the guys on the team, the front office and the ownership with the Mets. He will try to get to New York as quickly as possible."
A lifetime .292 hitter, Sheffield hit .291 with 34 homers and 123 RBIs with the New York Yankees in 2005, culminating a seven-year span in which he batted .307 and averaged 35 home runs and 110 RBIs.
Sheffield batted .247 and averaged 22 home runs and 66 RBIs in two seasons with the Tigers.
He was batting only .178 in spring training before his release.