The 18-year-old's original one-month deal expired at the weekend but he has now put pen to paper until January 3.
German has made six appearances for the League Two Shrimpers and scored one goal in the FA Cup draw against Macclesfield.
"He's shown glimpses of what he is capable of during matches but I believe there is more to come and which he will hopefully show over the next four weeks," said Southend boss Paul Sturrock.
Rangers have included a 24-hour recall clause in the deal.
Source: PA
Source: PA