The Spanish League leaders, with a perfect record in four matches this season, entertain the islanders at the Nou Camp determined to put their indifferent European form behind them.
But some supporters, who have seen their team lose 3-2 to Newcastle and then draw 2-2 with PSV Eindhoven on Wednesday in their opening Champions' League matches, fear Barcelona could crumble when faced by one of Spain's tough teams.
Tenerife, in fifth place, have former the Barca forward Meho Kodro upfront and have squeezed draws out of their last two games visits to Barcelona.
Local fans even hold the team in some affection since the Canary Islanders effectively handed Barcelona the title in 1992 and 1993 when they Real Madrid in key games.
Van Gaal tried four different defensive systems in Wednesday's match but failed to stop the Dutch side coming back from letting in two Luis Enrique goals - despite being down to 10 men.
To make matters worse, the game was just 15 minutes old when Barcelona's Brazilian striker Sonny Anderson limped off. He was examined by a doctor on Thursday, and the injury appears serious.
That is made worse by the fact that Hristo Stoichkov, his natural replacement, is out of contention after clashing with Van Gaal.
Real Madrid, fresh from a 2-0 win at Porto, should overcome Deportivo La Coruna tomorrow - on current form few would bet against Jupp Heynckes' men.
Real are lying in third position, behind Mallorca, the surprise team of the league, on goal difference.
Unlike Barcelona, the reigning champions have already had a tough fixture in the league this season - the derby with Atletico that ended 1-1.
Deportivo have not won a point in the Santiago Bernabeu stadium in the last five seasons despite being ever-present title challengers and they have lost their way this season after the departure of the Brazilian, Rivaldo, to Barcelona.Reuse content