Madrid slumped 13 points adrift of Barca on Sunday after being held to a home draw by struggling Espanyol and then seeing Tito Vilanova's men brush aside second-placed Atletico Madrid 4-1 at the Nou Camp.
Madrid coach Jose Mourinho admitted after the Espanyol game that it would be "practically impossible" to now retain their title, and with Barca having dropped only two points all season, it is tough to see how the nine-time European champions can claw back the difference.
However, if they do end up losing their crown to Barca, Madrid will be determined not to hand it to their arch rivals on a platter.
Benzema told France Football magazine: "I hope we can give chase to Barca. It will be tough, but we haven't said the final word on this."
Madrid will be desperate to make amends for their Espanyol setback and end 2012 on a winning note this weekend, but it will not be easy for Mourinho's men as they must travel to fourth-placed Malaga.
Malaga have already beaten the likes of AC Milan, Zenit St Petersburg and Valencia at home this season and another high-profile scalp on Saturday would see them move to within two points of Madrid.
While Madrid's problems this season continue to mount, Barca remain in dominant form at the top of the standings.
Sunday's victory over Atletico was their ninth on the trot in La Liga and saw them open up a nine-point gap over the rest of the field.
They then announced in midweek they had secured key trio Lionel Messi, Carles Puyol and Xavi on long-term contracts.
Argentina superstar Messi, who has scored a record-breaking 90 goals in 2012, is now tied to the Catalan giants until 2018, while Spain internationals Xavi and Carles Puyol have agreed extensions until 2016.
Barca travel to promoted Real Valladolid on Saturday.
The final round of Primera Division fixtures before the winter break started on Thursday night with three matches. Espanyol, Rayo Vallecano and Real Socieded recorded home wins over Deportivo, Levante and Sevilla respectively.
On Friday, Atletico take on Celta Vigo while Valencia will look to bounce back from their first defeat under new boss Ernesto Valverde when they welcome Getafe to the Mestalla.
The remaining matches are on Saturday, when Real Betis take on Real Mallorca, Osasuna face Granada and Athletic Bilbao play Real Zaragoza.