The 35-year-old third baseman participated in a simulated game before Saturday's game against the Philadelphia Phillies. He faced Anthony Swarzak and Tim Peterson and hit an opposite-field homer to right-center off Peterson for his only hit.
Wright has not played in a major league game since May 27, 2016, due to neck, back and shoulder injuries that required surgery.
"I think so," Wright said when asked if he thought the Mets would clear him to play this year. "The communication has been fantastic."
Wright hit .171 with two RBIs in 41 at-bats during 12 games of a minor league injury rehabilitation assignment from Aug. 12-29.
"Where he got to at the end of the 20 days was not where we thought he needed to be," Mets assistant general manager John Ricco said Friday. "Honestly, it does get more difficult to foresee a situation where he could come back to that level."
Wright intends to have another simulated game on Tuesday, then meet with chief operating officer Jeff Wilpon, a son of owner Fred Wilpon. Jeff Wilpon watched Saturday's session.
"The last thing that I want to portray is that there is some sort of rift between the Mets and I. That's false," Wright said. "There's been communication, and I know where they stand and they know where I stand. So the communication, especially recently, has been fantastic, and I look forward to meeting Jeff in the coming days and formulating a game plan from here to the end of September."
A seven-time All-Star, Wright has salaries of $20 million this year, $15 million next season and $12 million in 2020, the final year of his deal. If the Mets reinstate him from the 60-day disabled list, it would likely diminish the amount of insurance money they could collect on his contract.
"There's been an open dialogue and, obviously, I want to play, and understandably there's some hurdles that I have to clear before that," Wright said.
Wright fielded grounders in addition to hitting.
"I'd like to have some better at-bats," Wright said.
Mets manager Mickey Callaway was impressed with Wright's defensive footwork and his throws across the diamond.
"You can see some things. More importantly, it's David feeling things and him knowing that he can go out there and perform," Callaway said. "He's played a ton of major league games. He's going to know when that time comes."
The rookie manager understands how much of a different club the Mets could have been with Wright.
"We would have been a much, much better team because of his leadership and his ability to play this game," Callaway said.
Wright was on the disabled list from April 15 to Aug. 24, 2015, when he strained his right hamstring and then developed spinal stenosis. He returned late that season, as the Mets won their first National League pennant since 2000. But he has not played for them since May 2016; Dr. Robert Watkins operated that June 16 to repair a herniated disk in Wright's neck.
After Wright's rehabilitation was slowed by shoulder pain last season, Wright had surgery Sept. 5, 2017, to repair his right rotator cuff, and Watkins performed a laminotomy in early October in which a bony layer over the spinal canal was removed to treat nerve compression.