It has been almost 20 years since the Spanish capital's second club mounted a genuine challenge for the La Liga crown as Barca and Real Madrid, the world's two richest teams by income, have shared the spoils apart from brief flurries of success from Valencia and Deportivo La Coruna.
Last season's third place was the best Atletico had managed since they won a league and King's Cup double in 1996 and they even spent two seasons in the second division at the start of the millennium.
Current coach Diego Simeone, a former Argentina midfielder who was in the 1996 team, has revived memories of those glory days since he took over at the end of 2011, honing a mean defence and getting the best out of players like forward Diego Costa and midfielder Koke.
Atletico, the King's Cup holders, have won all their matches at their Calderon stadium this season apart from the first leg of the Spanish Super Cup in August when they drew 1-1 with Barca.
Victory on Saturday (1900 GMT) would put them three points clear of the Catalan giants with half the season played, while Atletico's city rivals Real Madrid are five points behind in third and play at Espanyol on Sunday (1800).
Koke, who earned a call-up to the Spain squad last year, has played a key role in Atletico's resurgence, developing a lethal partnership with Costa and netting some important goals himself, including the winner in Saturday's 1-0 victory at Malaga.
However, beating Barca to head the standings at the halfway stage of the campaign would be a mere "anecdote" as what counted was the state of play at the climax of the season in May, he warned on Wednesday.
"It is irrelevant if you win this match if in the end you have not achieved your objectives," he told a news conference that coincided with his 22nd birthday.
One man who will be itching to spoil Atletico's party is World Player of the Year Lionel Messi, who came off the bench and scored twice on his return from injury in Wednesday's 4-0 last 16, first leg success at home to Getafe in the Cup.
Lionel Messi was given a rousing ovation by the adoring home fans when he replaced Andres Iniesta in the 64th minute at the Nou Camp, the Argentina forward's first appearance since straining a thigh muscle in November.
The injury was the latest in a string of problems that dogged him during 2013 but he said he was now "free of pain" and full of desire to help Barca in their bid for La Liga, Champions League and King's Cup glory.
"I am as excited as ever," he told Barca's TV channel after the Getafe game, adding that he would consult coach Gerardo Martino and club medical staff to decide if he can start against Atletico.
"Before I had got used to playing with pain and today... I felt very good physically," the 26-year-old said.
"Beyond the injuries I just want to play again. If I can be in the team (on Saturday) I will be there."
Real have their King's Cup last 16, first leg at home to Osasuna to negotiate later on Thursday before they travel to Barcelona to face mid-table Espanyol, while Monday's game sees European hopefuls Villarreal, in sixth, hosting fifth-placed Real Sociedad (2100).