Lukaku has been heavily linked with the Italian champions for the past few days despite interest from Inter Milan.
The deal seems all-but done for him to swap Manchester for Turin.
The newspaper reports that the Belgium international could move to Italy with attacking midfielder Paulo Dybala going the other way to United in a swap deal.
The deal now seems inevitable and would suit both clubs.
DAILY POST reported yesterday that Lukaku will earn €9million (£8.2million) per season, a very similar offer to the one he received from Inter Milan.