Tosun, who joined the Blues from Besiktas in January for a fee in the region of £28 million, has had tough time so far on Merseyside - failing to nail down a spot in Sam Allardyce’s starting line-up.
Instead, Tosun has fallen behind Oumar Niasse in the pecking order with many fans wanting to see more of the 26-year-old who impressed for the Black Eagles in this season’s Champions League campaign.
Yet the door is open for a return to Istanbul if he so wishes.
“Cenk Tosun is like one of our sons,” Albayrak told TRTSpor in Turkey.
“We have a special place in our hearts for him. Yes, we are still in contact with him and if he tells us he wants to return our door is open. I am, however, sure he will return to form.”
The 26-year-old has only made four Premier League appearances since joining Everton, with two of those coming off the bench in defeats away to Arsenal and Watford. He was an unused sub in both the recent home wins over Leicester City and Crystal Palace.
It’s unlikely that the forward gives up on his Premier League career so quickly after joining, especially as he hasn’t been able to truly prove himself.
After joining Everton, Tosun said it was his ‘biggest dream’ to be playing in the Premier League and that he hoped to ‘become a role model’ for younger players in his home nation who want to make the step abroad.
He netted 14 times in 28 appearances for Besiktas before making the move to Merseyside and given the chances, he may be able to prove his worth - especially if a new manager at the club gives everyone a clean slate in the summer.