United enter Saturday's game against Millwall three points behind the Londoners, who travel to Bramall Lane sixth in the table.
HRH Prince Abdullah bin Musa'ad bin Abdulaziz Al Saud recently launched an attempt to take full control of the club in response to a process instigated by his fellow co-owner Kevin McCabe.
With a variety of issues, including the need to acquire United's property interests, complicating the process, Wilder appeared to express concerns about its timing before Tuesday's victory over Middlesbrough.
Speaking at his pre-match press conference this morning, Wilder said: "I shouldn't be talking about that now.
"I only will when the time is right.
"I'm an employee of this football club.
"I'll always be honest and open with the supporters and the board."
Wilder, who was responding to a question about the matter from a member of the media, went on to confirm Richard Stearman is set to resume training this morning.
The defender missed the meeting with Middlesbrough and last weekend's derby with Barnsley after tweaking a hamstring against Cardiff City earlier this month.
Striker Ched Evans has also "returned to the group" following a fitness issue.
"Richard should be back today," Wilder said. "That's good news for us."