The 23-year old Japanese striker joined the Lions from J.League club Kashima Antlers in January and has since scored four goals and provided two assists in nine league outings.
Osako has ambitions to play in the German Bundesliga but Funkel wants him to continue developing with 1860 who are currently sitting ninth in the 2.Bundesliga.
"He is not an unknown quantity anymore,” he told Bild.
"I personally believe that another year would do him good here. He has used the time since January to acclimatize in Germany.
"Now he could take the next step here. But he and his advisers will already know what to do…"
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