BBC and Daily Mail claim the 52-year-old Ajax manager is seen as fitting the profile the United board want for the man who they hope will restore the glory days the club enjoyed under Alex Ferguson.
The Mail says United held talks with Ajax -- whose chief executive is former United goalkeeper Edwin van der Sar -- at the end of last week about the conditions under which Ten Hag can leave.
His contract is up at the end of next season and would cost United around £1.6 million ($2.1 million) to prise him away whereas PSG might demand a far larger sum for Pochettino to leave.
However, Pochettino's position at PSG is far from secure after a disappointing exit in the last 16 of the Champions League -- the yardstick by which coaches at the Qatar-owned club are measured.
Ten Hag -- whose Ajax side were denied a place in the 2019 Champions League final in the final minute by Pochettino when he managed Tottenham -- has been interviewed by United and is said to have demanded backing from United to pursue his transfer targets.
According to the Independent newspaper, Ten Hag told United's football director John Murtough and technical director Darren Fletcher he envisaged a "five-year project".
He also addressed the futures of several present squad members, saying they are nowhere near "Champions League shape."
However, according to the Independent, he has "not blown people away" at United due to a perceived lack of charisma -- which reportedly saw him lose out to Nuno Espirito Santo for the Spurs job last summer.
In that respect, Pochettino comes out way ahead of Ten Hag, although he has been more muted at PSG than his passionate performances on the touchline when at Spurs.