Asked whether the friendly could form part of a wider tour of China, DFB secretary said this was "conceivable."
"The players didn't like it. I am very frustrated. Nobody had fun today," said Leno, who conceded twice in the opening 11 minutes of the match.
Schweinsteiger contacted Babak Rafati, 46, who made an attempt on his own life while still working as a referee in November 2011.
Jonker replaces Valerien Ismael, who was fired on Sunday after a 2-1 home loss to Werder Bremen left them only two points above the relegation zone.
Cologne sporting director Jorg Schmadtke has said he is eager for the "madness" of the Chinese Super League transfer window to end.
The struggling Volkswagen-backed club said in a statement that Ismael was leaving "with immediate effect" and that a new coach would be named soon.