The Red Devils boss has already informed deal maker Ed Woodward the players he would like to bring to Old Trafford.
Atletico Madrid forward Antoine Griezmann, Monaco midfielder Tiemoue Bakayoko and Inter Milan winger Ivan Perisic are targets.
Mourinho wants at least four new signings to strengthen his squad.
And he believes the club will succeed in completing 'interesting' deals.
"It's very important to get signings done early and the board knows that," Mourinho said.
"But I also know that the market is very difficult, so I'm not a silly manager to say, 'I give the names and you have to give me the players.'
"I give the names, the options, I give the second options in case the first are not possible. But I give all the information based on my analysis, based on my experience and my projections for the future. But our relationship is very, very good.
"First of all they know not asking for impossible targets, I ask for difficult targets. Then it's a difficult job and they try to do the best they can.
"I'm sure that by the end of the summer we probably don't have exactly my first options, because difficult to succeed with every attempt.
"But I'm sure we're going to do something interesting and to improve our team for next season."
