The 27-year-old agreed a new contract with Dortmund last season. But before he penned the extension, Blaszczykowski had a minimum fee release clause that prompted interest from City.
The Premier League giants were shopping around for a winger earlier this summer, eventually bringing Spain international Jesus Navas to the club from Sevilla.
But, according to Blaszczykowski, they also sounded out his interest.
Speaking to Polish newspaper Przeglad Sportowy, the Poland international said: "Dortmund simply had the advantage over Manchester City.
"We have a great squad, fantastic manager, incredible supporters and a very bright future ahead of us.
"In Dortmund, me and my family have everything we need. I did not pursue interest from other clubs in my services."
The Champions League finalists have endured a tough summer so far, with Mario Gotze departing for Bayern Munich and Robert Lewandowski seemingly keen to follow.
They've made a few signings of their own though, including St Etienne forward Pierre Emerick Aubameyang and Henrikh Mkhitaryan from Shakhtar Donetsk.