Chelsea say they have not made an offer for Kaka, despite claims from AC Milan vice-president Adriano Galliani that they made an "astronomical" bid.
The Blues have long been linked with a move for the 26-year-old world player of the year and their boss is now ex-Brazil coach Luiz Felipe Scolari.
Galliani told Italian newspaper La Stampa: "We received an astronomical offer from Chelsea for Kaka."
But BBC Sport understands Chelsea have not made any bid for the Brazilian.
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The AC Milan vice-president also revealed there has been interest in their 29-year-old Italy midfielder Andrea Pirlo.
Pirlo's agent has been reported as saying in the Italian press he wants his client to be given the same wage as Kaka.
But Galliani added: "For Pirlo, there have been many requests but neither Pirlo nor his agent have come into my office and asked me for an improvement in salary."
Galliani says selling Kaka and Pirlo would immediately stabilise Milan's finances, with the club having missed out on a place in next season's Champions League.
"All we would need to do in order to wipe out our debts is sell Kaka and Pirlo," he said.
AC Milan technical director Leonardo reiterated that Kaka would not be leaving the San Siro under any circumstances.
Last month the Brazilian told BBC Sport it was "impossible" for Chelsea to sign the player. "I can only repeat what we keep saying - there is no possibility of Kaka moving away from Milan," Leonardo said.
"We have not received an official bid for him. He is very close to AC Milan and has a very, very good relationship with the club."
Kaka himself revealed to BBC Sport in April he would not rule out the possibility of one day playing for one of the big clubs in the Premier League.
New Chelsea boss Scolari will meet up with the current squad on Monday when the players return for pre-season training.
On Sunday he toured the Cobham training ground and met key members of staff.
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