Fuel was added to speculation over Hernandez's future at the weekend when, on his verified Twitter account, a link was retweeted to a story in which his fellow Mexico international Carlos Vela suggested the 25-year-old should look to leave United if he does not start playing more regularly.
Hernandez has made only one Barclays Premier League start this term and, although he scored three times in the two games prior to Saturday's top-flight win at Fulham, he was an unused substitute for the clash at Craven Cottage.
May admits that, with Wayne Rooney and Robin van Persie currently very much on form in the United attack, the present situation is difficult for Hernandez.
But he is far from convinced that switching clubs would be the best thing for the ex-Guadalajara frontman.
May, who is supporting the Manchester United Foundation Chevrolet Trax eBay auction, told Press Association Sport: "It is difficult, because are you going to leave Wayne out? Are you going to leave Van Persie out?
"But whenever he (Hernandez) has come in, he has done great.
"There is talk that he's going to have to leave and go somewhere else to get first-team football ahead of the World Cup (next summer). But he'll get plenty of games (at United), I'm sure he will.
"Probably at the moment, though, Wayne and Van Persie are the first two names on the teamsheet - and rightly so, because they have been unplayable at times."
Asked if he would urge Hernandez to stay even if things stay the same, May - a United player from 1994 to 2003 - added: "It depends where he could go - you'd have to see the teams he might go to.
"But for me, he is at the best the club in the world and he will get games and plenty of minutes on the pitch. Wherever else he goes, for me it would be a step down.
"I don't think he will play a bit-part role for United - I think he will play a massive part.
"If Wayne or Van Persie gets injured, he can step in, take over the mantle and carry on scoring goals."
The man who now determines how much game time Hernandez, who joined United in 2010, gets for the Red Devils is boss David Moyes, following his appointment as successor to his fellow Scot Sir Alex Ferguson over the summer.
In the Premier League, the team are beginning to build some momentum after a shaky start to the campaign, but in the Champions League - where Moyes is lacking in experience - the results so far have been solid.
United head into Tuesday's away match against Vela's Real Sociedad having beaten the Spanish side 1-0 at Old Trafford in their last European outing, and drawn at Shakhtar Donetsk and beaten Bayer Leverkusen at home in their two other Group A games.
May, who was part of the United squad that won the 1999 European Cup, is not about to tip United for the crown this season, but he is also not surprised that the team have fared well so far, despite the change of manager that has occurred.
"I think it is a big ask for David Moyes to take us all the way," the 43-year-old said.
"There are probably better teams out there than United at this present time.
"The Germans are very strong and Barcelona and Real Madrid are going to be there or thereabouts, so to actually get to the final and win it would be a tough ask. All teams need that little bit of luck as well.
"But it doesn't surprise me where we are right now.
"David Moyes might not have a lot of experience, but the players he has taken over - look at Ryan Giggs, Rio Ferdinand, Nemanja Vidic, Robin van Persie.
"Those type of players have an absolute abundance of experience in the Champions League."