The Gunners have had discussions with Leipzig, but have yet to make a formal offer for the Slovenia international.
This delay has opened the door for rivals to step in, with Chelsea expressing interest in Sesko.
The Blues are looking to add a second striker to their squad, and Sesko is one of the options being considered, along with Eintracht Frankfurt's Hugo Ekitike.
Arsenal's manager, Mikel Arteta, is taking his time to evaluate Sesko's skills and compare them to those of Sporting CP's Viktor Gyokeres.
