All summer reports have suggested that the 24-year-old French international could join Cesc Fabregas in vacating the Gunners.
However, when asked about a potential deal which would see Nasri join City, Cook decided against providing an update on the situation.
"We always try not to disclose anything - obviously he's still an Arsenal player and we need to respect that," Cook told Sky Sports News.
"So unfortunately I will refrain from giving an update."
Earlier today Nasri branded Arsenal supporters "disrespectful" for chanting against him on Saturday.