The German outfit go into the second leg of their semi-final two goals adrift after a woeful performance on home soil last week when they were eventually flattered by the margin of defeat.
It leaves Rangnick clutching at the smallest of straws as his side bid to book a final meeting with Barcelona at Wembley on May 28.
Talking a good game: Ralf Rangnick insists his Schalke players must believe they can beat Manchester United
But he knows it can be done, as United proved in the Nou Camp 12 years ago and Bayern also managed when they got their revenge in last season's quarter-final after initially falling three goals behind.
'We have to be well organised and take our chances when they are presented,' said Rangnick, whose squad was delayed at Dusseldorf airport after finding visas had not been issued for five of their players, including strikers Edu and Jefferson Farfan, plus Japanese defender Atsuto Uchida.
Listen up: Boss Rangnick (centre) gives his Schalke players their instructions in training at Old Trafford
'Even if there are just two minutes leftwe still have to think about United and in 1999 when they were a goal down going into injury-time and they still managed to win.
'You can never tell what will happen in football. Things can turn around so quickly, and United's match against Bayern last year is another example.'
Schalke also have their impressive 5-2 win over holders Inter Milan at the San Siro as a reference point.
New home? Schalke keeper Manuel Neuer, who has been linked with United, trains at Old Trafford
Young defender Benedikt Howedes was fit for that one and after two games out with an abdominal strain, Rangnick is considering picking the 23-year-old to face the Red Devils.
'The last four games he played we won,' he said. 'But this is not the last game of the season.
'He has to be 100 per cent fit and we will listen to the medical staff because we don't want to take a risk and find out that he will be missing for another three or four weeks.'
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