Cooper scored in his 1860 Munich debut but struck just once more in his next 11 appearances before being sidelined with a knee injury in November.
In an article headlined, "Brazen -- Papa Cooper wanted starting spot guarantee," Bild newspaper quoted 1860 Munich coach Ewald Lienen as saying:
"Kenny and his father came to me and wanted more playing time. They were clearly worried about Kenny's World Cup participation. But I couldn't promise that. Up to a couple of days we didn't even know whether he was fit to play. So they both asked for a move. We agreed, because an unhappy player doesn't help us."
The move comes at an inconvenient time for 1860 Munich, which faces a striker shortage.
"About Kenny I have absolutely nothing bad to say," Lienen said. "If there were difficult talks, it was with his father."
Kenny Cooper played one game (12 minutes) for the USA in the 10-game final round of 2010 World Cup qualifying -- a 2-2 tie with Costa Rica after the USA had already clinched a spot in South Africa. He has scored two goals in 10 games since debuting for the USA in 2007.
Plymouth Argyle is third-from-last in the English League Championship (second division).