The Brazilian international, 24, is not being targeted as a replacement for Luis Suarez with the Anfield club intent on keeping their want-away star.
Atletico are considering the bid for Costa having sold Radamel Falcao earlier in the summer to Monaco for £50m and brought in David Villa as a replacement from Barcelona.
Costa is keen to speak to Liverpool, who recruited Iago Aspas earlier in the summer from Celta Vigo for £7m, as Rodgers looks to get more goals into his team.
Diego Costa is not being targeted as a replacement for Luis Suarez
Atletico Madrid sold Radamel Falcao this summer
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Suarez has six matches still to serve on his suspension for biting Branislav Ivanovic and Daniel Sturridge has not featured in pre-season as he continues his rehabilitation from an ankle injury.
Sturridge will not play in Steven Gerrard's testimonial tomorrow, but still hopes to be fit to face Stoke on the opening weekend of the season.
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