The 25-year-old played under Rosler for Brentford, and the paper report the new head coach is hoping to strike a £500,000 deal.
Moore has a contract until 2017 at Cardiff, and started the season off as second choice for the club.
An ankle injury to David Marshall in January gave Moore his opportunity, playing 10 Championship games and conceding 14 goals, with one clean sheet.
Cardiff bought Moore from Brentford in 2013 for £150,000, but he has made just 15 appearances for them.
A transfer move for Moore would raise questions over Marco Silvestri's future at Leeds, but with veteran Stuart Taylor released, the club need an alternative at the position.
Alternatives could include former goalkeepers Paul Robinson, who told the Lancashire Telegraph he would be open to a switch to Leeds, or Scott Carson who played under Uwe Rosler at Wigan.
Another option is Southend stopper Daniel Bentley whose penalty shootout heroics helped the club win the League Two play-off final yesterday at Wembley. He was previously scouted by Brian McDermott, reported The Mail, and when owner Massimo Cellino attended the Morecambe v Southend game earlier this month it was speculated it could have been to watch the goalkeeper.