According to Kicker, Augsburg are in advanced talks for the 22-year-old and will pay around €3m.
Highly-rated Gumny has been called up by Poland several times, but is yet to win his first cap.
Gumny will solve a problem for Augsburg with Raphael Framberger currently their only specialist right-back.
Augsburg have now completed the signing of Gumny on a five-year deal.
Neuzugang am Start: Der #FCA verpflichtet den polnischen U21-Nationalspieler Robert #Gumny von @LechPoznan. Er erhält einen Vertrag bis 2025. Willkommen in der Fuggerstadt, Robert! ✌ ℹ Alle Infos ➡ https://t.co/aZUjbwqncC pic.twitter.com/JYIqqXBne0
— FC Augsburg (@FCAugsburg) September 2, 2020