Davidson, 53, said although he was friendly with Wyness he had only asked him for "advice and assistance" about football clubs before agreeing to buy the 93.7% share in the Spanish La Liga team earlier this month.
"I do wish him well. It is a great loss to the club. It is a great loss to Everton."
Davidson said he had spoken to Wyness about football clubs because he had been a "success" and he believed it would not be long before he had another job.
"He has not been asked to join the club."