Mallorca have not conceded a goal in four league matches and with an away goal under their belts, are odds-on favour-ites to go through.
The winger Neil McCann is expected to play a key role because of his ability to take on defenders. The Mallorca coach, Hector Cuper, has already stated that the Scotland prospect is the man he fears most.
Jefferies said: "If we get past Mallorca it will go down not only as one of Hearts' best results in Europe, but one of the best performances by a Scottish club at this level.
"The tie is not finished at 1-0 and I know they respect us. We are an excellent side on the break. I am aware they have not conceded a goal this season but that run has to end soon, perhaps today. But we must also be a little bit cautious in our approach. We can't go too daft.
Jefferies has been heartened by the progress of injured goalkeeper Gilles Rousset and midfielder Stevie Fulton. Rousset is expected to return after missing the last two matches because of a back problem, while Fulton is showing good improvement from a hamstring injury. Hearts will be backed by up to 5,000 supporters, a mixture of regular fans and Scottish holidaymakers.
"It will be almost a home game for us," said Jefferies. "Mallorca have a very passionate support so it should be a great atmosphere."
The club chairman, Leslie Deans, is so thrilled at the support the Scottish Cup winners are getting, he took out a half page advert in the English language Daily Bulletin to welcome them to the island.
Ironically Mallorca's support base is dwindling. Today they will be without injured keeper Carlos Roa and midfielder Ariel Ibagza.Reuse content