Warnock was dismissed on Sunday evening after a bad run of results which have left the newly-promoted side 17th in the Premier League table.
Beard believes that an appointment needs to be made soon in order to use the January transfer window to the club's advantage.
"I'm not going to comment [on candidates] tonight but what I will say is that we're going to move as quickly as we can and we hope to make an appointment very soon," he told Sky Sports News.
"Time is against everybody and we're already into the second week of January. I think the reality is there are some funds there but we've got to make the right purchases.
"It is a tricky month to try and make things happen but our appetite is to bring one or two players in if we can to strengthen the squad and the new manager will be part of that as soon as we can identify him and spend time looking at some of our targets."
Click here to see Sports Mole's list of contenders for the Loftus Road job.