Wilder, who led Sheffield United to the top flight, is one of the bookmakers' favourites to replace Scott Parker at Bournemouth.
But Wilder made it clear he would be staying in the north-east to carry on building up Boro.
He said: "I'm not going anywhere. I've got my head down and am working towards the weekend.
"I signed a two-and-a-half-year deal nine months ago so I'm deep into that and I enjoy working at this football club.
"The focus for me has been on the rebuild, players coming in and preparing the team. You can't stop speculation - you just have to ride with it."
On Tuesday night, Watford delivered a 2-1 comeback win over Middlesbrough. Muniz, the on-loan Fulham striker, headed home his first Boro goal from a cross from Ryan Giles in the fourth minute but Watford were level 20 minutes later.
Pedro's run down the left had Boro in knots and he cut in to find Sarr in the box. The Senegal forward, who had seen a move to Aston Villa fall through earlier in the month, turned to bamboozle a defender before slotting home.
"Everyone knows that those two players shouldn't be playing at this level because they have undoubted super quality," Wilder added.
Bayo's winner came shortly after Muniz had tried to lob Watford goalkeeper Daniel Bachmann. Mario Gaspar's deflected effort fell kindly to the summer signing and Watford were able to celebrate.
"A shanked shot that fell to their boy and he tucks it away, it was the perfect ending for their team but it wasn't something we deserved to happen," Wilder said.
"I don't think we were outplayed at all and in the second half looked the most likely to win it."