The 25-year-old has been linked with an £8m switch to the Liberty Stadium recently, and Monk says that a deal is close but will not be completed in time for Saturday's trip to Manchester United.
"We've had good chats with Federico, the fee has been agreed and we're just agreeing personal terms," he told reporters.
"Hopefully he'll be coming over this week for a medical. It won't be done in time for Saturday."
Fernandez made four appearances for Argentina in this summer's World Cup and could become the Swans' sixth signing of the summer.