The Southend United midfielder is a long-term target for Sheffield United.
The Sheffield United boss confirmed his side have made a fresh attempt to sign Leonard, who was a target for the Blades during the summer transfer window.
Southend have continued to rebuff the Championship side's advances for the player, but could be more inclined to sell him now with his contract up in six months' time and promotion looking unlikely at this stage.
And according to Wilder, they can either take or leave the one that is currently on the table.
When asked if Sheffield United would return with another offer if Southend say no again, the 50-year-old replied: "No.
"We've made an offer, so we'll give a deadline to that. I want to get players in early January, I don't want to go through January and look towards the end of it. I don't want that situation to happen.
"We've got some big fixtures in January, so we're looking [for] the three or four players that we're looking to bring In, across the positions that we want, we want done early.
"Hopefully we'll be able to do that and can get those in place [by] 1 January to move on into the month."
Sheffield United are especially keen to strengthen in Leonard's area of the pitch, having lost Paul Coutts to a broken leg.
And given recent reports linking the Blades with a renewed approach for Fleetwood Town's Devante Cole, it would appear as though a new striker is also on Wilder's radar.
Will Sheffield United finally get their hands on Ryan Leonard in January?