Argentine striker Aguero, 22, has been linked with a move to Stamford Bridge before, and is regarded as one of the most exciting talents in La Liga
Chelsea are known to be in the market for a centre-half and could view Uruguayan Godin as an alternative to David Luiz whose club, Benfica, are holding out for a fee of £25m.
Atletico’s majority shareholder Miguel Angel Gil said: “In the last week, we have received two offers. One from Real Madrid for Aguero for £39m and the other from Chelsea for Aguero and Diego Godin for £52m.”
The champions last night refused to comment on the claims, a spokesman saying: “We never comment on transfer speculation, no matter how wild it is.”
Meanwhile, after Monday’s 4-0 win at Bolton, captain John Terry believes critics of his side should be fearful.
He said: “The message is you don’t fear us at your own peril. We’ve never been out of the title race.”