The Turkey Under-19 international has won rave reviews since breaking into the Super Lig club's first team last season.
Omur, who can operate in central midfield or on the right wing, has played regularly for the Black Sea coast club this term.
Tekelioglu said: "Arsenal want to sign Abdulkadir.
“Arsene Wenger does a good job when it comes to discovering young players.
"Abdulkadir will be a success when he moves to Europe."