Those at Old Trafford are starting to piece together summer recruitment plans.
Senegal international Gueye has proven himself as a Premier League performer in a holding role.
Those efforts are said to have caught United’s eye, but Silva is reading little into the gossip.
The Toffees boss said when asked about the Red Devils rumours: “It’s news to me.
“[We have] no concerns about that or all the other speculation in the media that will come in the next few days or weeks.
“It’s something natural but I’m not here to answer all the possible rumours.
“What is important to me, if you’re asking about Gana, is how he’s performing well, how he’s helping our team with full focus, working hard every day to perform like he did in the last game.”
While reluctant to speculate on Gueye’s future, Silva is prepared to admit that he would like to keep loan stars Kurt Zouma and Andre Gomes on his books once season-long agreements with Chelsea and Barcelona come to a close.
He said on the futures of a French defender and Portuguese midfielder: “There’s always a chance but it’s not something that is just in our hands.
“They are happy here which is a good sign, that means they are performing, they are enjoying and they are helping us.
“We are happy with them, it’s up to us to do what we can to keep them and it’s up to the clubs, also. And it’s up to them, it’s not just in our hands.
“It’s in the players’ minds and decisions after their own clubs. They have to decide together. In the right moment, we’ll do something.”