The 33-year-old outfielder with two Gold Gloves led the majors with a combined 47 stolen bases last year with Miami and Oakland and then signed as a free agent with the Mets before the lockout.
But Marte has been affected by a left oblique ailment that has prevented him from hitting at all during the team's first week of spring training camp. The team is taking a careful, cautious approach with him.
"We haven't had anything negative [on Marte]," Mets manager Buck Showalter said. "With an oblique, if you come back too quick from that, it turns into a long-term thing. He came with it. He didn't get it here."
Marte's skills make him a fit for the leadoff spot in Showalter's batting order. Lefty-hitting Brandon Nimmo, who batted first in Sunday's spring training game against St. Louis, is the other option at the top of the order.
Both are also competing for the starting spot in center field, with newcomer Mark Canha -- a right-handed batter like Marte -- also in the mix.
"Nimmo is a good outfielder. I'm the same thing, Canha the same thing. Anywhere we need," Marte said.
Showalter said he feels good news is on the way with Marte as the club prepares for opening day on April 7 in Washington.
"Just his progression," Showalter said. "Obviously, I know more than I'm going to say here, but I don't want to put him in a position where we get to 26 hours from now we think he'll do that and he isn't able to do it."
"He's in great hands, and he's not taking any steps back. He's able to handle everything we're progressing with," he said. "We're hoping in the next few days to have something to tell you about him offensively."