The 20-year-old has been a key player for his Portuguese club during the 2021-22 campaign, making 44 appearances in all competitions, contributing five goals and two assists in the process.
Inacio still has more than four years left to run on his current deal, but there is believed to be a €45m (£38.5m) release clause in the agreement, which Sporting will demand in full in order to allow him to leave.
According to A Bola, Man United have identified the youngster as a leading transfer target and are prepared to meet the buy-out fee in his deal to secure his signature, with incoming head coach Erik ten Hag viewing him as the ideal player to boost the team's defence.
The report claims that the 20-time English champions are preparing an offer which would see Sporting receive an initial €40m (£34.2m), with the further €5m (£4.2m) in add-ons.
Inacio, who has also been strongly linked with Newcastle United, has been with the Green and Whites since 2012, progressing through their various youth teams before making his senior debut in 2020.
The Portugal Under-21s international has made 69 appearances for his current side in all competitions, contributing seven goals and four assists in the process.
This term, Inacio has featured on 27 occasions in the league, contributing four goals and one assist, while he played on seven occasions in the Champions League before the Portuguese side were eliminated by Manchester City in the round of 16.
Man United are believed to be determined to add another centre-back this summer amid the uncertainty surrounding Harry Maguire's future, while Eric Bailly, Phil Jones and Axel Tuanzebe could all potentially leave the club in the upcoming market.
Maguire has struggled for form during the 2021-22 campaign and could have the captain's armband taken away from him by incoming manager Ten Hag.
However, the England international is likely to remain at the club, with Victor Lindelof and Raphael Varane also set to stay, but the possible departures of Bailly and Jones would leave the 20-time English champions short of centre-back cover heading into the new campaign.
The Red Devils have conceded 56 Premier League goals this season, with only Southampton (61), Newcastle United (61), Watford (70), Leeds United (74) and Norwich City (75) having poorer defensive records.
Man United will miss out on Champions League football for the 2022-23 campaign and are instead battling West Ham United for a spot in next season's Europa League, with Ralf Rangnick's side currently sixth in the table ahead of their final game of the season away to Crystal Palace.