Malky Mackay looks likely to complete his second signing of the summer, following the arrival of striker Andreas Cornelius in June, with the defender set to discuss personal terms
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."