Juan Ignacio Martinez's side have fared impressively at continental level this season, finishing second in Group L behind Hannover after three wins, two draws and one defeat from six matches.
But after emerging from a pool that also featured Helsingborg and FC Twente, Levante can expect a step up in class in the first leg against Olympiacos in Thursday night's Europe League last-32 tie in Valencia. The Greek side who have dropped into the Europa League after finishing third in their Champions League group.
Olympiacos won three and lost three of their Group B matches to finish just a point behind second-placed Arsenal, and will feel confident that Europe's second-tier competition provides a possible route to success this season.
Martinez needs everything to go in his favour if Levante are to progress and at least has a fully-fit squad at his disposal after David Navarro recovered from a thigh problem picked up in last weekend's home defeat to Malaga - a result which marked Levante's fourth loss in their last five La Liga outings.
The hosts will be without suspended Sergio Ballesteros, however, while fellow defender Loukas Vyntra, a recent signing from Olympiacos' domestic rivals Panathinaikos, is cup-tied.
Greece international Vyntra joined Levante on a free transfer on January 31 having spent 10 years at Pana, and has seen enough of Olympiacos in that time to have no doubts about the threat they pose.
"Olympiacos are a team with a lot of experience in European competition," said the 32-year-old, who made his Levante debut in the defeat to Malaga.
"It will be a very difficult game for both teams but we hope to win."
Thursday's match is first between Levante and Olympiacos in official competition, but that lack of familiarity should not be a problem for the Greek side's new coach Michel, who knows Spanish football inside out.
The former Real Madrid midfielder replaced Leonardo Jardim as Olympiacos boss earlier this month and boasts a wealth of experience in the Spanish game, having won six league titles with Madrid. He has also coached at Rayo Vallecano, Getafe and Sevilla.