The Bluebirds want to sign the Liverpool right-back, who has made just five appearances for the Reds this season, and hope to get a deal done quickly.
They moved three points clear of the Premier League relegation zone with a 1-0 win at Leicester on Saturday. The transfer window opens on Tuesday and Warnock is eager to bolster his squad to aid Cardiff's survival bid. '
He said: "We've got nine or 10 concrete enquiries in at the moment, obviously we're not going to sign them all.
"But you've got to do that, we're looking to strengthen this team. Results like this will help me, we're not adrift at the bottom of the table.
"People might think, 'I don't want to go to a team at the bottom of the table' but it's difficult to bring players in. I won't do it if they're not better than the ones we've got, even though I know we need a bigger squad.
"We spoke about Clyne months ago, but then he got back into the Liverpool team against Manchester United, then they had a few injuries, so things change.
"But honestly, we've got nothing set for any position at the moment, I'm hoping that changes this week."