United are rumoured to be in the market for Luis Alberto, Sergej Milinkovic-Savic and Ciro Immobile.
However The Mirror report that Lazio director of football Igli Tare has warned the Red Devils that the trio are not for sale.
All three have starred to help Lazio to third in Serie A, behind Juventus and Napoli.
Barcelona are also reported to be on the hunt for Alberto, who previously had a disappointing spell at Liverpool.
Mourinho is keen to bolster his midfield with Michael Carrick retiring this summer and doubts over the future of Marouane Fellaini.
However Barca see Alberto as a replacement for Andres Iniesta who is departing this summer.
It is also claimed that United’s Premier League rivals Tottenham are interested in Milinkovic-Savic and Immobile.
Spurs boss Mauricio Pochettino is reportedly planning a major overhaul of his squad after another season without silverware.
Forward Immobile would fit at both Manchester United and Tottenham, who primarily play just one up front.
Manchester United are rumoured to be selling both Anthony Martial and Marcus Rashford this summer, leaving Romelu Lukaku as their sole striker.
Harry Kane is Tottenham’s main threat with the likes of Vincent Janssen and Fernando Llorente failing to provide sufficient competition to the England international.
