Bluebirds boss Dave Jones targeted Russian midfielder Alexei Smertin on a season-long loan before the transfer window closed on Monday but the 33-year-old rejected a move to south Wales.
A secondary window opens for domestic emergency loan deals next week.
And Jones said: "I will be working with the chairman to bring a midfield player in on loan."
Ramsey made a total of 22 appearances for Cardiff, including a substitute appearance in last season's FA Cup Final against Portsmouth at Wembley Stadium.
Before choosing Arsenal, the Welsh prodigy spoke to Manchester United boss Sir Alex Ferguson as the Premier League and European champions looked favourite to sign him.
They were Cardiff's preferred choice as they would have had a loan-back agreement.
But Ramsey chose north London and told BBC Wales last month: "It's a massive step up from the Championship level.
"I found it quite tough in the first week, but now I've settled in a bit."
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