The holders travel to the Spanish capital on February 18 in the hope of reaching a third consecutive Champions League final.
Domestically, Atletico are struggling and find themselves sixth in LaLiga - 13 points off leaders and bitter rivals Real Madrid.
But, according to Spanish publication Marca, the club have been boosted by the 'surprising presence' of Costa during training.
The Spain international has missed the last two-and-a-half months of the season as he undergoes rehab after thigh surgery.
But the report claims he is showing ‘incredible desire' to return for the clash with Liverpool, with his return being described as 'fundamental' to saving Atleti's season.
Alvaro Morata and Joao Felix are both currently injured, leaving Diego Simeone bereft of attacking options.
But Costa's return could prove timely, especially considering his personal battles with the Reds during his time at Chelsea.
The 31-year-old infamously clashed with both Jordan Henderson and Steven Gerrard during his time with the Blues as he lifted two Premier League titles.
Diego Costa has made a surprise return to Atletico Madrid training with the sole intention of making a Champions League comeback against Liverpool