The Hoops currently have only two fit central defenders in Erik Sviatchenko and Efe Ambrose and they are facing Wednesday's Champions League signing deadline to register new players for the third qualifying round of the tournament.
The Scottish giants will first have to turn around the 1-0 deficit against Gibraltar minnows Lincoln Red Imps in the second leg of the qualifying tie on Wednesday.
Blackburn Rovers defender Shane Duffy and free agent Kolo Toure, formerly of Liverpool, are two leading names that have been linked with the Hoops recently but Rodgers has been unable to make a transfer breakthrough in the central defensive department just yet.
"It's a big concern but that's what we have," Rodgers said.
"Ideally, we'd want to try to at least have one more in by the deadline.
"I want it now – but it doesn't always work out that way.
"Is it realistic? I'd hope so. It won't be the fault of this club if not. The club are doing everything they can to support my needs."