Morosi added the San Diego Padres have also shown interest in the veteran starter.
Morosi noted the Mets "aren't soliciting offers," and the cost "would have to be high" if they were to move Syndergaard.
Despite entering the All-Star break with the National League's second-worst record (40-50), ESPN's Buster Olney reported the Mets are indicating to teams they will wait a little longer before determining if they will become buyers or sellers.
The Brewers seem likely to be in play for every available starter this summer. Their rotation ERA of 4.82 ranks 19th in MLB and has played a role in their bullpen throwing the fifth-most innings (369) in the first half.
Houston has a terrific trio at the top of its rotation with Justin Verlander, Gerrit Cole and Wade Miley. Brad Peacock is on the injured list with shoulder discomfort. Collin McHugh was moved to the bullpen after posting a 6.37 ERA in eight starts at the beginning of the season.
Another reason for the Astros to pursue Syndergaard is because Cole will be eligible for free agency after this season. They turned Cole into one of MLB's best pitchers after acquiring him from the Pittsburgh Pirates in Jan. 2018, so there would be reason for them to think they could get Syndergaard back on track.
Syndergaard's price tag is going to be high because he's under team control through 2021. The 26-year-old has been inconsistent this season with a 4.68 ERA and 101 strikeouts in 105.2 innings.