Atletico are level at the top with champions Barca on 46 points with just under half the season played, with Real five further back in third.
With La Liga's leading marksman Diego Costa in scintillating form, the capital's second club are in a strong position to match Valencia's feat from 2004 of denying Spain's wealthy big two the domestic title.
Argentine Simeone, who has transformed the club since taking over at the end of 2011 and led them to a King's Cup triumph against Real last season, told Italy's Il Giornale daily that one of his wishes for 2014 was the La Liga crown.
"It would be stupid not to think about it, above all looking at the standings," he told the newspaper.
However, the health of his three sons was the most important thing, added the 43-year-old, who spent part of his playing career at Serie A sides Inter Milan and Lazio.
He also had two stints at Atletico and was part of the side that won a league and cup double in 1996.
As well as riding high in La Liga, Atletico are through to the last 16 of the Champions League, where they will play AC Milan.
They will meet Valencia over two legs in the last 16 of the King's Cup, with the first leg at the Mestalla on January 7 and the return at the Calderon a week later.
Atletico have yet to play Barca in La Liga but beat Real 1-0 at the Bernabeu in September, their first league victory against their bitter city rivals in more than a decade.