"I don't want to get into the specifics of it, but he's tested positive, he is recovering and we feel like he's in a good position [of being ready for the season]," Van Wagenen said, per Scott Thompson of SNY.tv.
"We'll wait and see once we get everybody here in camp."
Van Wagenen did not say whether the player will land on the "COVID-19 Related Injured List" that Major League Baseball instituted for this season.
"The protocols obviously are fairly extensive to protect not only the individual who has the virus but also the rest of the teammates and the coaches," Van Wagenen added.
"We'll continue to follow that protocol outlined by baseball. We're optimistic that the player can return as early as the start of camp or hopefully soon there after. It's just so hard to predict with this virus."
Six Mets minor leaguers have also tested positive for COVID-19, per Van Wagenen.
Players for all 30 MLB franchises are expected to report Wednesday for what MLB is coining "Summer Camp," which will be the ramp-up period acting as a second spring training of sorts before the regular season begins on either July 23 or 24 for all teams.
Practices will begin Friday in teams' home ballparks.
MLB has instituted various safety protocols amid COVID-19. Of note, there will be no pregame sharing of lineups, and social distancing rules will be enforced on the field where applicable.
For example, base coaches are not allowed to leave their coaches' boxes and speak with players, and managers can't come within six feet of an umpire to argue. Violations carry punishments including a game ejection, fines and suspensions.