The 27-year-old Inter Milan midfielder has been heavily linked with a move to Old Trafford all summer following the retirement of Paul Scholes. But the boss maintains arrangements to acquire the Dutch international have not been made.
"There's no real interest at this moment in time in Wesley Sneijder for a lot of reasons," said Sir Alex at a press conference in Seattle.
"I've not really been involved in it since we've come to America. So there's nothing I can tell you about it. I couldn't tell you [what's happening]."
Sir Alex was quizzed further about any other potential new signings to add to the three he has already made this summer - Phil Jones, Ashley Young and David de Gea. But the manager insists there is nothing new to report on that front.
"Nothing's imminent at this moment in time. Obviously we're trying but we've signed three players and we're very comfortable with that," said Sir Alex.
"We've signed Phil Jones, Ashley Young, David de Gea and they're three tremendous young players to add to the squad I have from last year. We've also got people coming back from loan periods like Danny Welbeck, Tom Cleverley, Mame Biram Diouf and Federico Macheda.
"We've filled the gaps we've needed to fill. But the one we're having difficulty replacing is Paul Scholes, which is always going to be hard.
"I don't think we'll find a Scholes but we'll find a different type of player because Manchester United do that. Time and time again we've faced this problem when we've lost great players. Eventually