The 40-year-old quickly became a fan favourite in Germany after registering six goals and three assists after arriving at the club in January.
Schalke's sporting director Frank Baumann said conversations were still ongoing with Dzeko but his future could only be finalised once he has played at the World Cup, where the forward will represent Bosnia.
"I think Edin of course also notices what he can give to the team and the club - but just as much what the club can give to him," Baumann explained.
"He made a very conscious decision there: that he wants to play, that he wants to experience something positive and that he can also end the season with such a highlight.
"Of course he also has a World Cup ahead of him and is now also not exactly the youngest anymore, but we have agreed that we will sit down together after the season. But there will be no deadline from our side.
He further emphasised that the tournament schedule would affect the timeline regardless: "Due to the World Cup, he won't be on the pitch on the first day of training anyway, and that's why we have time."
Aston Villa are pushing to complete a deal for Joao Palhinha and have stepped up their efforts to sign the Bayern Munich midfielder, following his stint at Tottenham last season.
Bayer Leverkusen have completed the signing of defender Facundo Medina from Olympique Marseille, the Argentina international penning a five-year-deal with the Bundesliga outfit.
Bayern Munich have completed the permanent signing of Senegal midfielder Bara Sapoko Ndiaye from Gambinos Stars, with the 18-year-old signing a contract until June 2031.
Sead Kolasinac experienced a nostalgic return to the VELTINS-Arena on Saturday, lining up for Atalanta against his former club Schalke 04 in a friendly.
