Atleti head into Saturday's contest with a two-point lead over city rivals Real Madrid at the top of the table.
They know that a victory will guarantee their first top-flight title since 2013-14, when a 1-1 draw at Barcelona on the final day denied the Catalans the trophy.
However, the stakes are also high for Valladolid, who must win to stand a chance of avoiding relegation to the second tier.
History is on Atleti's side: Valladolid have not won any of their past 11 league meetings and failed to score in seven of the previous eight, while Sergio Gonzalez has gone eight LaLiga games without defeating Simeone, more than he has against any other head coach.
Simeone could become only the third Atletico coach to deliver two top-flight titles after Ricardo Zamora (1940 and 1941) and Helenio Herrera (1950 and 1951), so he could be forgiven for feeling the pressure.