The Blades manager wants to bring the former Oxford United wideman to Bramall Lane on loan.
But, Boro are reluctant to allow 27-year-old Johnson to leave until they bring in new signings of their own.
With the loan transfer window due to close next Friday, Wilder accepts he must stay patient. with several other Championship clubs keen to sign Johnson.
Wilder confirmed: “It seems everybody knows about Marvin Johnson, so it’s no good me trying to hide away from it.
“Yes, we have made an enquiry about Marvin. We have been speaking to Middlesbrough, like a couple of clubs have made enquiries about a couple of our players who have not been playing.
“There is an interest from us on that. We have to wait for other clubs to do business to allow us pursue what we want to do.
“We have spoke to Middlesbrough, there’s been a couple of other enquiries from other clubs, and we understand that. Talks are ongoing.
“It’s fair to say Middlesbrough have been in the market for a few players recently, and Tony (Pulis) is in the same situation as I am.”
United hope to bring in Johnson and a striker before Friday's deadline, but Wilder has denied he is looking at Millwall’s Lee Gregory.
The former Blades Academy youngster - who made his name at FC Halifax Town - netted 10 goals for the Lions last season, and is a proven scorer at Championship level.
But Wilder said: “Lee has not been on our radar, he’s a really good player and a connection with Sheffield United.
“He’s done a fantastic job at Millwall, but is not someone we have enquired about.
“It’s not a permanent from our point of view, we haven’t got the finances to do that, it will be a loan deal.”