The Valencia-based side continued their fairytale maiden European campaign last Thursday with a 1-0 away win over Olympiacos that sealed a stunning 4-0 aggregate triumph over the 39-time Greek champions.
That set up a last-16 showdown with Rubin Kazan, who knocked out holders Atletico Madrid, but before they take on the Russian side next month Juan Ignacio Martinez's men will attempt to fix their poor domestic form.
In their last seven matches in Spain Levante have lost five times and won just once, a run that has seen them knocked out of the Copa del Rey and drop down to ninth in the standings.
Levante are still 14 points above the relegation zone, but Martinez is keen to ensure that gap does not get much smaller.
He said: "We aren't going to lose our concentration, because our bread and butter is the league, where we have to achieve safety.
"Now we face a very difficult game against Osasuna. When the game against Rubin is closer, then we'll look at that one."
On Monday Levante play host to an Osasuna side who are in the thick of the relegation dogfight, but gradually working their way towards mid-table. They have picked 11 points from their last six matches, with their only defeat coming at the hands of runaway league leaders Barcelona.
That improvement has lifted Jose Luis Mendilibar's side up to 16th spot, five points above the bottom three.
Experienced defender Ruben is remaining grounded though, warning his side they still have a long way to go yet.
"We've done nothing so far, because with the points we have at the moment we would be down at the end of the season," he said.
"We are steadying our position, but there's still a lot to do."
Looking ahead to the clash with Levante, who Osasuna beat 4-0 at home earlier this season, midfielder Emiliano Armenteros said: "They are strong at home. They've been playing in Europe this week but I think they have enough time to rest until Monday.
"They've been a very solid team for several years, well organised and who can cause a lot of damage on the counter-attack. It'll be a game where anything can happen."