The 25-year-old 6ft 3in front-man has netted 33 league goals in 101 appearances since arriving from Nuremberg in 2006.
And the forward, who has won two caps for Germany to date, is currently the leading scorer in the Bundesliga this season with six goals, firing Leverkusen to top spot on goal difference.
As a result, reports have surfaced linking him with a move to pastures new during the winter transfer window.
And the player's representitive, Ali Bulut, has confirmed that Arsenal, as well as Bayern Munich, AC Milan and Juventus are all monitoring his progress.
“He is becoming a big player and things are working for him at the moment," he told Sport.co.uk.
"He is a very similar player to Rudi Voller with a bit of Oliver Bierhoff. Six or seven big clubs have been in contact including England and Spain's top clubs, plus Bayern Munich.
"For four years Arsenal tried to loan Kiessling from Nuremburg, but it wasn't possible. Now, and in the future it might be possible.
"Arsenal, Bayern Munich, Juventus, and Milan are the clubs that have shown an interest. I think it is likely he will spend another year in Germany, but he wants to move to a big club, and after that I don't know.”
