The Egypt international joined Boro from Cairo club Al Ahly in 2007.
The 27-year-old is under contract until next year.
“I will not complete my contract at Boro,” insisted Shawky. “I will start from now to search for a new club.
“I haven’t received any offers yet, but I have huge hope that they will arrive in the coming period, especially from English clubs, who now know my abilities.
“Mido underwent a lot of injustice at Middlesbrough. He was the best striker in the squad and its top scorer, but despite this he was not played regularly.”