Reports suggest that the Spanish club have turned down an offer from the Red Devils for the 21-year-old midfielder because they are unwilling to sell.
Spanish football expert Guillem Balague was responding to a question on Twitter when he revealed that United had an approach rebuffed by Atleti.
"The truth is that there has been an approach," he wrote.
"United offers €20m but Atletico not selling ATM."
Saul, who has represented Spain at all youth levels, has also recently been linked with Arsenal and Liverpool but it appears as though Diego Simeone has no plans to get rid of the talented youngster anytime soon.