The Red Devils are reported to have agreed a world record £100m transfer for the 23-year-old Frenchman.
Pogba left Old Trafford in 2012 as a 19-year-old, with the Italian side paying a tribunal fee of just £800,000.
"I am not going to try to make you naive and believe that we are not trying for one player," said Mourinho.
The Portuguese manager has made three signings so far this summer, bringing in defender Eric Bailly from Villarreal, midfielder Henrikh Mkhitaryan from Borussia Dortmund and striker Zlatan Ibrahimovic.
When asked about the possible signing of Pogba, Mourinho replied: "We set four targets for us, we got three of them and we are going to get the fourth.
"We established the profile of four players to improve the squad, to give us more options, especially adapted to my way of thinking about football.
"Everybody speaks about one, but it wouldn't be a surprise for me if it is not him and it is another one because we went for profile.
"We have two more options in front of us and we are going to close one."
