Arouna Kone's second-half strike earned Levante a 1-0 win at the Ciutat de Valencia in September - one of only two defeats suffered by Jose Mourinho's men in La Liga this term.
Madrid head into this weekend boasting a seven-point cushion at the summit - although Barcelona could reduce that when they visit Osasuna on Saturday - but Iborra reckons fourth-placed Levante should not be written off.
He told club website www.levanteud.com: "If we could beat them at home, why not there?
"It will be difficult, but if we did it earlier in the season why not now? If the team performs as we want, we can get something there."
Levante have not won in the league since beating Sevilla 1-0 on December 10, but Iborra is convinced the six-game winless run is just a blip.
"We must show the strength that we are known for, and we can make a good game of it," he said.
"We need to regain the positive feelings and break this streak.
"This is a small bump, but it was not normal how many points we had. It was normal that there would be a downturn at some point. We must move forward. We look forward to the Bernabeu in search of a good result."
Madrid midfielder Xabi Alonso urged his side to concentrate only on their own performances rather than worry about their advantage over Barca.
"We're not obsessed about the difference in points between us and Barcelona," the Spain international told www.realmadrid.com.
"We shouldn't change the way we do things. We must go little by little and win each game in the coming weeks, in which we'll play less matches."
Barcelona coach Pep Guardiola accepts it will be "very difficult" for his side to overhaul Madrid but promised there will be no let-up in their pursuit.
"It's normal that in La Liga we're below a team like Real Madrid," he said on www.fcbarcelona.cat after last night's Copa del Rey semi-final victory over Valencia. "We're in a tough situation in the competition.
"It'll be very difficult to reach them. We have to force them to win it. We have to put pressure on them. In the end, these players challenge themselves."
Third-placed Valencia will return to league action on Sunday against Sporting Gijon with Los Che coach Unai Emery seeking victory to avoid equalling his worst winless streak at the helm.
Emery's side have not triumphed in the league since beating Malaga 2-0 on December 18, but will have their work cut out this weekend against a Sporting team looking to impress new interim coach Inaki Tejada.
The 46-year-old was last week placed in temporary charge of the Asturians following the departure of Manuel Preciado. He oversaw Sunday's 1-1 draw with Osasuna and was this week told he has until the end of the campaign to prove his worth.
Sevilla will also be looking for an upturn in fortunes under a new coach, with Michel having been named Marcelino Garcia Toral's successor on Tuesday.
The Andalusian side have picked up just two points from the last 21 on offer, and were last weekend beaten 2-1 at home by relegation-threatened Villarreal.
Former Real Madrid midfielder Michel's first match in charge of Sevilla will be Monday night's trip to San Sebastian to take on Real Sociedad.
In other games this weekend, Racing Santander host Atletico Madrid and Real Betis face Athletic Bilbao on Saturday, while on Sunday fifth-placed Espanyol play bottom club Real Zaragoza, Malaga tackle Real Mallorca, struggling Villarreal host Granada and Getafe visit Rayo Vallecano.