Both Premier League clubs had scouts present for Inter's pre-season derby with AC Milan in Perth to run the rule over the 21-year-old, who Inter value at around £73m, reports The Sun.
The 6ft 3in striker passed his big-stage exam with flying colours, with glowing scouting reports said to have landed on the desks of Arsenal boss Mikel Arteta and his Manchester United counterpart, Michael Carrick. Esposito, who made his senior debut for Italy last season, scored ten goals and provided six assists in 48 appearances across all competitions in his breakthrough campaign at the San Siro.
Arsenal's coaches have reportedly been monitoring the Italy international for months, with Arteta keen to add attacking options behind Viktor Gyökeres and Kai Havertz. The Gunners' business up front has stalled elsewhere this summer, with Gabriel Jesus expected to leave amid interest from AC Milan and other Italian clubs, while Arsenal missed out on a move for Vinícius Júnior after the Brazilian agreed new terms with Real Madrid.
Arteta is understood to want a physically dominant focal point capable of bullying Premier League centre-backs while working hard for the team, attributes Esposito is seen to fit.
Manchester United have also been tracking the striker for some time but have no intention of rushing into an offer, having compiled an extensive dossier on the player without feeling any immediate need to table a formal bid.
Old Trafford chiefs are willing to sanction Joshua Zirkzee's exit and want another forward option behind Benjamin Sesko, but are likely to wait for Inter Milan to soften their stance before moving. Inter, for their part, have publicly declared Esposito "untouchable" in an attempt to ward off English interest, with the club having previously moved to reassure supporters that no approach from Arsenal had been accepted as they build their attack around the forward following his breakthrough into the first team.