The New Year transfer window opened at midnight amid a flurry of rumours.
With just six points separating 10th-placed Aston Villa from third-bottom Spurs, Birch is well aware of the dangers as he enters what will be a crucial month for Leeds.
"There has been a varied interest in Mark Viduka but I have said all along that I would like to try and keep this squad intact," Birch said in the Yorkshire Post.
"It is important Leeds United remain in the Premiership and to survive we need to retain our best players if we can.
"Of course, it becomes a different kettle of fish if somebody slaps in a transfer request. We do not want to keep players here who are unhappy, no matter who they are.
"I took the decision to keep the squad together when I was at Chelsea and it paid great dividends for us then because the club was a more attractive proposition to potential buyers. It is important we keep our nerve, maintain a cool head and think carefully about the long-term future of Leeds United. If we sell today just because the cash is being waved in our faces then we could regret it tomorrow.
"The loans we already have at the club will stay for the remainder of the season but there is a chance that Eddie Gray might be able to look at bringing in one or two more loan players," he added.
"That, unfortunately, would be the extent of it though, there would be no money to spend on buying players unless the white knight we have been looking for rides in with his millions."
"It is good to know that we have the ability to bring in one or two loan players but I cannot see anything happening straight away," Gray commented.
"I have been looking, you must always be aware of what is available, but there does not seem to be much out there at the moment.
"I will only bring in players who I feel will do us a decent turn, players who can add to what we already have and there are few of them available at the moment."
Gray has just over four weeks to conclude his search before the transfer window closes at 5pm on Monday, February 2nd.