Ozil, who has not played for Arsenal since March, professed his love for the Istanbul-based outfit in a Q&A session this week.
And Emre confirmed the club had a meeting with Ozil and his agent about a potential move to Turkey.
"I look very positively on behalf of the community and the president, but I do not see it easily. We have plans of our own," Emre told reporters.
"Mesut also has a contract with his club. He is a superstar. We are talking about a player who contributed to a goal in every other game at every club he has played for. I would be very pleased if Fenerbahce could have such a player.
"We had a meeting with him and his manager. Mesut is closer than ever. The fact that Mesut had this childhood dream and Fenerbahce had the dream has made this step so close for the first time.
"After the meeting process with Mesut's club is over, we will hold meetings between ourselves. If Mesut agrees with his club on the terms we want, it won't stretch our financial limits this year.
"Fenerbahce and other clubs no longer have to power to bring in footballers on €4-5 million contracts. There will be no numbers that would disturb the balance or affect the salaries of other players, we do not have that ability."