"Everton approached him and he said no to Everton," Balague said in a video posted on his YouTube channel.
"Why? Because he is thinking of Arsenal. He has been told Arsenal are interested in him."
Pressure has been mounting on Everton boss Sam Allardyce in recent weeks, with a growing number of supporters calling for him to stand down at the end of the season.
Fonseca has been tipped as a frontrunner to fill the void, but the former England boss claimed during a recent press conference that he will be in charge next season.