But he has words of comfort for Jones.
"You may have been to Old Trafford before and played there and you know it is going to be bigger than a small club like Blackburn, but it is not until you are in there that you realise how massive the club is," May told the Manchester Evening News.
"I was over-awed by the size of the place. I walked into the dressing room where there were title and cup winners like Peter Schmeichel, Paul Ince, Mark Hughes, Roy Keane and Eric Cantona. All huge characters.
"It is an awesome situation to go into, but I can assure Phil then you get used to it. Your character eventually comes through and you start to feel more comfortable.
"I don't know Jones, but to have impressed the way he has in the Premier League as a 19-year-old means you have to have a certain strong character about you.
"Despite the names and achievements of the players around, when I joined they were all still very welcoming and I am sure Phil will find that in the current dressing room.
"It's all about the team at United and they want players to come in and feel part of it. That helps with the spirit.
"In terms of what he is walking into, you could not find anything better anywhere. You have the best boss in the business in Sir Alex Ferguson and the best players in the Premier League. You cannot buy that kind of experience.
"For a new player going to a place like Old Trafford, you could not have it better to settle you in and get you playing your natural game.
"Even though I was awestruck at first, I eventually warmed to it and fed off it. I am sure Phil will be looking forward to it in the same way and will benefit from it.
"The other great thing he'll get is patient backing from the United fans and that is absolutely vital. They stick by their players at Old Trafford. The support trust the manager's judgment and they are very, very patient. That is a huge help for any young newcomer."