The Turkey midfielder was thrust into the HSV starting line-up in November due to the absence of the injured Rafael Van der Vaart, and responded by scoring against Wolfsburg and Hannover in the Bundesliga.
His form has reportedly led to him being monitored by the Premier League pair, and the 19-year-old appeared to be flattered by the attention from the Gunners, describing them as “interesting” to Sky Sports.
However, HSV sporting director Oliver Kreuzer was adamant that no official enquiry had been made by any club, and revealed his intention to offer Calhanoglu a long-term renewal on his existing terms.
“We want to extend Calhanoglu’s [contract] until 2018 in the near future,” he said to the Hamburger Abendblatt.
“To date, no club from England has made contact with him. Of course, every player has a price. But we do not have any interest in selling him.
“It is not our goal to make money from Hakan. That would be for us a big step backwards. [He] is the future, and should remain at HSV. He is keen on making a name for himself in the Bundesliga.
The German-born midfielder has scored four times in 14 appearances during the Bundesliga campaign, and made his international debut for Turkey earlier in 2013.