Carrick, who was confirmed as United's permanent head coach on a two-year contract on Friday, has been involved in recruitment discussions throughout his interim tenure. Di Marzio reports that United have now shifted their focus specifically onto Tonali, with the Italy international the player Carrick most wants to bring to Old Trafford as he prepares for a return to Champions League football.
Tonali, 25, has been a consistent presence for Newcastle United this season, making 53 appearances across all competitions including 11 in the Champions League. He is expected to be available this summer after Newcastle finished outside the European places, with the two parties understood to have a gentleman's agreement that he would be allowed to leave if the club failed to reach the top four.
Newcastle's valuation is in the region of £86 million. Di Marzio reports there is a "good chance" a deal will go through, with the fee potentially structured as €80 million (£69 million) plus bonuses rather than the full €100 million figure Newcastle have set as their asking price.
Manchester United are also in discussions with Atalanta over midfielder Ederson, with reports in Italy suggesting a fee of around £46 million has been agreed. Carrick is keen to add both players to replace Casemiro, who plays his final game for the club this weekend before leaving as a free agent.
Arsenal's interest in Tonali has also been reported, and Manchester City remain in the background, though Di Marzio suggests United believe Tonali will be convinced by the prospect of a clearer starting role at Old Trafford in a side returning to Europe's top competition.
Newcastle are not expected to make the process easy. Selling a key player to a direct Premier League rival rarely goes smoothly, whatever the paperwork says.