Diego Simeone's table-toppers travel to Catalunya for their final league game of the season three points clear of second-placed Barca, knowing a draw would be enough to claim their first league title since 1996.
Should they avoid defeat this weekend, Atleti will secure the first part of a potentially historic double, with the capital club set to face neighbours and arch-rivals Real Madrid in next Saturday's Champions League final.
There had been concern that Costa - who has scored 36 goals in all competitions this season - could be absent for both games, but the 25-year-old is now back in training and, according to Miranda, is desperate to fire Atleti to glory.
"He's raring to play - he knows how important this is to us and he'll be on form to do his stuff," he told Marca.
Barca will retain their Liga crown with a win on Saturday, as that result would give them a superior head-to-head record over Atletico.
But Simeone's side have held something of a hoodoo over the reigning champions this term, having won one and drawn four of their five meetings in the league, Champions League and Super Cup.
And Miranda is confident that Atleti are fully prepared to extend that unbeaten run this weekend.
"They'll come out strong and we will have to stay tight at the back because I'm sure we'll score a goal against them," he added.
"To beat Barcelona, we have to play with a lot of intensity, to play well physically. We've been preparing for it very well all week and will arrive 100 per cent ready."