TMW says the negotiations are being held independent of Chelsea's interest in Napoli star Victor Osimhen.
Napoli and Chelsea are currently thrashing out terms for Lukaku over a fee of €25-30m. A further €5m bonus is also being discussed.
There is now a confidence of an agreement between the two clubs, which could also lead to Osimhen being sold to Chelsea.
Napoli sports chief Giovanni Manna said yesterday on Osimhen: "That this blocks the market as (Antonio) Conte said is an objective fact. Victor is an important player with important parameters, and his will is clear. We were keen to preserve the integrity of the group and we made a shared choice.
"Now we'll see what will happen in the next few days. Giving sensations today is not correct, we are working with his entourage to find the best solution. I repeat, he is a player with important parameters, he is not a player who simply needs to be fixed. He has a contract for another two seasons. If a solution is not found by August 30th we will have to speak to the boy."