Speaking after his side's 2-0 win over Ajax in the Europa League final, Mourinho played down the possibility of a move.
"I think not. Honestly, I think not," he told Sport TV.
"But you never know. Good players are always welcome."
United secured three trophies in 2016-17, adding the Europa League to the EFL Cup and Community Shield.
While Wednesday's win secured United's place in next season's Champions League, Mourinho said he knew what he wanted regardless of the result.
"The club knows perfectly well what I want. They knew two months ago. It had nothing to do with qualifying for the Champions League," he said.
"A giant club, but it's not a giant team. We need that second step, possibly the third one."
Along with Silva, United are also heavily linked with a move for Atletico Madrid star Antoine Griezmann.