Trailing 1-0 from the home leg, the pride of East Anglia need a result which has been beyond English clubs for more than 30 years. Even when Liverpool were pre-eminent in Europe, they never won here. Birmingham City managed it in 1960, but then the Fairs Cup was little more than a friendly tournament.
Norwich complete their preparations today uncomfortably aware that it is not only history that is against them. For a week now, either side of Saturday's 2-2 draw with Manchester United, they have been seeking ways of compensating for the absence of three of their most important players.
Ian Culverhouse, the sweeper, Ian Butterworth, an accomplished marker, and the playmaker, Ian Crook, are all suspended for a match in which only the best will do.
In the circumstances, Inter's pounds 40m team of all the talents must be the hottest favourites since. . . well, since Norwich made a nonsense of the odds by beating Bayern in Munich two months ago.
A repeat of the unflagging spirit, faultless organisation and splendid skill that had the Canaries soaring in the Olympic Stadium could see the Italians put to flight.
If Mark Bowen can deputise successfully for Culverhouse as sweeper, if Gary Megson can fill in for Crook as well as he did at Old Trafford, if Ruel Fox and Chris Sutton can combine as cleverly as they did to embarrass United for 30 minutes on Saturday - if all these questions have positive answers, it might just happen.
It is asking a lot. Probably too much of a team forced by suspension to reappraise the style of play which has served them so well.
Mike Walker, their tactical guru- cum-manager, considered abandoning the sweeper system here, in its spiritual home, because of the absence of Culverhouse and his second choice libero, Crook.
The problems posed by the unavailability of these two caused him to delay selection yesterday, but he hinted strongly that he would persevere with a spare defender, and Bowen is earmarked for the job.
'I have thought about changing the system,' Walker said, 'but against this sort of opposition, you need the extra man at the back. The security he provides can buy you the time and space to play.'
Inter did most of the playing at Carrow Road, where they were good value for the win secured by Dennis Bergkamp's second-half penalty. Fifth in Serie A, they come to the return after a 3-1 win away to Lecce.
Like Norwich, Milan's 'other' team are below full strength, but in their case the loss of one expensive international, injured, is counter-balanced by the introduction of another. Wim Jonk, the Netherlands' midfielder, has given way to Russia's Igor Shalimov, who scored twice at the weekend. Some substitute.
All the advantages lie with the big battalions, yet Walker is in perky mood. Why so confident? 'Twenty- four goals away from home this season,' he said, with a cheeky-chappie grin. 'Not bad, eh?'
Optimistic, yes. Cocky, no. 'They could beat us 3-0 quite easily - we know that. But we also know that if we get it right on the night, we could beat them 2-0, no problem.
'If we do win, it would be our greatest achievement. We're without three of our best players. If we get beaten, it's not the end of the world. We're still in with a chance of doing something in one or more of the competitions at home.
'It would then be a question of what happens next. Would we bottle it or would we go on and progress? I think they would go on.'
If he was beginning to sound like a man resigned to defeat, the impression was a false one. 'We're capable of beating them, and whatever happens we will go out and enjoy it. If we play, we'll give anybody a game.'
The heart says Norwich, but the head insists Bergkamp and Sosa are too good for their make-do-and- mend defence.
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