The Beard may be switching coasts.
Wilson, 30, underwent Tommy John surgery last April after two early-season appearances.
He has indicated he will be ready for Opening Day, although a major league source said the reliever is not yet able to demonstrate in workouts that he is back to pre-surgery form.
The source speculated that the Mets willingly would sign Wilson to a minor league deal now, but Wilson agreeing to such an offer seems a stretch. As a result, the negotiation process will continue.
USA Today had earlier reported Alderson watching Wilson's workout, which is believed to have taken place at UCLA.
Wilson was nontendered by the San Francisco Giants in November after earning $8.5 million in 2012.
The Mets need late-inning arms in their bullpen, although they already have closer Frank Francisco under contract for the upcoming season at $6.5 million.
Francisco underwent surgery in December to remove a bone spur from his right elbow, but Mets officials have suggested he will be ready by spring training.
Wilson, if he ultimately signed with the Mets, would provide manager Terry Collins with another late-inning option and would not necessarily unseat Francisco as closer.
Wilson is a three-time All-Star. His 48 saves in 2010 led the majors and tied a Giants single-season record. From 2008 through 2011, Wilson allowed only 15.1 percent of inherited runners to score -- the best rate in the majors.