Cardiff, who won the Championship last season, have struggled to strengthen their squad since being promoted to the Premier League.
|5/6||Cardiff are 5/6 with William Hill to finish as the top promoted club
However, Brayford's arrival appears imminent after a bid for the 25-year-old full-back was accepted on Thursday.
"Cardiff City Football Club can confirm that the club has had a bid for Derby County right-back John Brayford accepted by the Rams," read a statement from Cardiff.
"The player has now been given permission to discuss personal terms with the Bluebirds and undergo a medical.
"Brayford, who is entering the final year of his contract at Pride Park, expressed a desire to make the move and test himself at the highest level of football in the Premier League."