Trautmann, who was bestowed with an honorary OBE for his work in promoting Anglo-German post-war relations played more than 500 times for City between 1949 and 1964.
His feat in the 1956 FA Cup final became one of the legends of the tournament when he played the final 17 minutes of that game with a broken neck to ensure victory over Birmingham.
A City spokesman said on Friday they are planning a tribute to their former keeper, such as a minute's applause and armbands at their first home game of the season, and will also consider a more lasting recognition of his contribution such as a statue or facility being named after him.
The German FA (DFB) said Trautmann passed away at his home near Valencia in Spain on Friday morning.
DFB president Wolfgang Niersbach said: "Bert Trautmann was an amazing sportsman and a true gentleman.
"He went to England as a soldier, and thus a war enemy, and he became a celebrated hero there. He was a legend.
"His extraordinary career will remain forever in the history books."
In an interview two years ago, he admitted that being known primarily for that FA Cup final injury sometimes rankled - for him, becoming the first German player to play in an FA Cup final at Wembley a year earlier had rated much higher.
"That was something absolutely magnificent," he said. "We lost 3-1 to Newcastle United on the day and yes, you feel a little sorry for yourself that you lose such a huge game, but it was an amazing day and I just looked around the stadium and thought 'you lucky man!'
"Then, of course, we returned a year later and won, but of course many people remember the game because of the injury I sustained during the match.
"I played over 500 league games for City but that moment is still the one people refer to, so it can be a little frustrating at times because no matter how well I played during that time, people will still say 'ah, you're the fellow who broke his neck playing at Wembley'.
"I'll admit it's not something I particularly like but it's something I've had to live with."
As a teenager in Germany, Trautmann had been enlisted in the Hitler Youth, became a paratrooper and was captured on the Russian front. He managed to escape and was re-captured by Allied troops and sent to a PoW camp near Wigan, where he first start playing in goal.
After being released and marrying a local girl, he played for non-league St Helen's Town, and impressed in a friendly against City, who took him on despite knowing he would receive a hostile reception from opposition fans.
After his playing days, he moved into management with Stockport before returning to his native Germany in 1967 to coach Preussen Munster.
Joe Corrigan, one of Trautmann's successors as City's keeper, said the German had been a "friend and mentor" who helped him with advice after he had broken into the first team.
Corrigan told the club's website: "Bert was a fantastic man and was one of the greatest goalkeepers of all time, and I'm proud to have called him both a friend and a mentor.
"As a keeper, Bert had everything. He was agile, intelligent, commanding and brave and is a true legend in every sense of the word. A couple of years ago he wrote the foreword for my autobiography - the words he wrote still send a shiver down my spine."