Van Dijk has established himself as one of the worlds best central defenders following his £75 million move to Jurgen Klopps side in January 2018.
Mourinho, meanwhile, was desperate for United to sign a new centre-back in his final transfer window at Old Trafford, but the club refused to meet his demands and the Portuguese ended up getting sacked last December after a series of poor results.
According to The Independent, Van Dijks name was put forward as a potential signing before he eventually joined Liverpool but Mourinho said no to the possibility of bringing the Netherlands international to Old Trafford.
The report claims that Mourinho did not want to sign another central defender at that time, even though the 56-year-old changed his mind just a few months later and pushed for Ed Woodward to sign Harry Maguire from Leicester City.
Its also claimed that Uniteds scouting structure is in disarray with many reports on potential transfer targets going unread.