The 21-year-old, who has scored 10 goals in 10 games for the Danish club this season, had reportedly attracted interest from a host of Premier League clubs.
However, Magnus Agnar Magnusson told Sky Sports News: "Of course it is flattering for Aron to be linked with such a huge club as Arsenal.
"We all know that Arsene Wenger is a great coach to work under as he has proven to be able to get the best out of his young players for years, and of course it would be an interesting place for Aron to continue his development.
"That said we have heard nothing from Arsenal and at the moment we are concentrating on extending the deal with AGF. We are in regular contact with AGF and if they deliver an interesting enough proposal then we would be interested in extending the deal."
Johansson's contract expires at the end of the season.