Corriere dello Sport says a contract offer has been tabled by United to Icardi's representatives. The Argentine's current deal carries a €110m buyout clause.
Key to United's pursuit is super agent Mino Raiola, who is keen to work as an intermediary between the two clubs.
Icardi was expected to join Real Madrid last month, but after initially taking a preliminary medical, was left hanging by the Spanish giants as coach Zinedine Zidane vetoed the deal.
United are now in contact, but face competition from across Europe for Icardi's signature ahead of the summer market. Indeed, there is a belief inside Icardi's camp that Real will try again should Zidane move on.