Ernesto Valverde's side, who claimed the Copa del Rey by beating Sevilla 5-0 last weekend, are still unbeaten in the Primera Division and could claim the title before even taking to the pitch at Riazor on Sunday.
Here, Goal takes a look at everything you need to know ahead of Barca's match against Deportivo...
Sergi Samper is sidelined with a long-term injury, but Barcelona have an otherwise fully fit squad for the trip to Riazor.
Sergi Roberto is suspended after he was sent off in the 2-2 draw away to Celta Vigo, Barca's last league game before the Copa del Rey final.
Barcelona potential starting line-up
With the Copa won and no Champions League football left, Valverde will pick a strong side for the game at Deportivo on Sunday.
Luis Suarez and Lionel Messi will start in attack, with Nelson Semedo in for the suspended Sergi Roberto at right-back.
Andres Iniesta, who gave an emotional press conference on Friday to confirm he will be leaving the club this summer, will play in midfield where Paulinho, Philippe Coutinho and Sergio Busquets are also set to feature.
Deportivo team news
Deportivo's hopes of avoiding relegation are fading fast, with Clarence Seedorf's side down in 18th place ahead of the 35th round of matches.
Back-to-back 3-2 wins over Athletic Club and Malaga had given Depor a boost, but their last two matches (versus Sevilla and Leganes) have ended goalless and they are nine points behind 17th-placed Levante.
Defeat for Deportivo and just a point for Levante (who are at home to Sevilla on Friday) will see the Galicians relegated.
Eneko Boveda is sidelined for Seedorf's side, while Adrian Lopez, Sulley Muntari, Sidnei and Zakaria Bakkali are all doubtful.
TV channel & kick-off time
Deportivo versus Barcelona kicks off at 20:45 local time on Sunday and will be broadcast live in the UK (United Kingdom) on Sky Sports Football and also on Sky Sports Main Event from 19:40 BST.
In the United States, the game can be watched live on television on beIN SPORTS and kicks off at 14:45 ET.
Best Opta match facts
Deportivo have only won one of their last 15 La Liga games against Barcelona (drawn four, lost 10); 2-1 at Riazor last season.
The Galicians suffered their biggest defeat in La Liga history against Barcelona, an 8-0 loss at Riazor in April 2016.
Barcelona are the first team in La Liga history to go unbeaten in their opening 33 matchdays in a single season (with 25 wins and eight draws so far).
Leo Messi has scored 17 goals in his 16 games against Deportivo in La Liga. However, he hasn’t scored in his last two games against the Galician side.
Adrian Lopez has bagged four of the last five Deportivo goals in La Liga and has scored in two of their six games against Barca in the competition.