The former England coach applied for the Poland national team post after Michal Probierz's controversial exit.
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However, Kulesza has explained turning down Southgate, stating to Przeglad Sportowy: "We received an offer of his employment.
"But we must remember the basic issue: no foreign coach will give us a guarantee that we will advance to the world championship. If he gave us such a guarantee, I would hire him right away.
"Fernando Santos is a perfect example," Kulesza added. "Coach with success, big name, everyone applauded, and the verification was surprising and painful for all of us."