The Gunners have been linked with several strikers since failing to bolster their ranks in the January transfer window.
Arsene Wenger will be looking to reinforce a forward line which has become overly-reliant on Olivier Giroud during the course of the season, with the Frenchman cutting an increasingly weary figure in recent weeks. The back-up option in Yaya Sanogo has shown promise but has been thrown in at the deep end at a time when Arsenal need a marquee centre forward signing.
It would appear Chelsea have blown their competitors out of the water in the race for the coveted Atletico frontman, forcing Arsenal to look elsewhere in their search for a 20-goals-a-season striker.
Plenty of names have been thrown about with regards to a potential move, not least Julian Draxler whom Wenger feels can be converted into a central spearhead, while Jackson Martinez has featured prominently in rumoured shortlists.
Having baulked at Atletico's excessive demands for Costa in January, it remains to be seen what sort of figure Arsenal would have to pay to prise Mandzukic away from the Bundesliga champions.
Mandzukic will be in demand this summer, expected to lose his place in the starting lineup at Bayern due to Robert Lewandowski's impending arrival. Pep Guardiola is also thought to be eyeing two or three further new signings for his side, which will have ramifications on the future of Manchester United target Toni Kroos also.
While Wenger's future remains far from certain, with his contract up this summer, work is going on behind the scenes to ensure targets are obtained ahead of next season.
The report also adds that the Gunners are hoping to add two strikers to their ranks in the close season, with an understudy such as Salomon Kalou, Loïc Remy and Alvaro Morata also in the pipeline.
Mandzukic has top scored for Bayern in the Bundesliga this term and, ironically, only Lewandowski can match his tally of 17 goals.