Aside from the pair, United have had tentative links with Real Madrid's Raphael Varane, Bayern's Jerome Boateng and Milan Skriniar from Inter Milan but they remain outsiders for the moment to strengthen the heart of the United backline.
"The atmosphere is good but if I was them I wouldn't come", United boss Mourinho was quoted as saying by BBC Sport at his post-match press conference.
Nevertheless, it raises a familiar question as to whether or not the Portuguese tactician should be questioning his players publicly, which is something that he hasn't been afraid of doing throughout his career but particularly in spells with Chelsea and Man Utd.
Mourinho told beIN SPORTS: "I am confident I will get one, but I think two I am not going to get which is not a drama".
Many of United's best players have been on holiday since the World Cup, where players such as Lukaku and eventual victor Pogba played late into the tournament and were subsequently in need of a rest.
"They would like to have here Golden Ball victor Luka [Modric], but it is what it is and it's hard for every club with lots of players in national team".
"Alexis is the only attacking player we have", said the United manager.
"We don't have wingers, we don't have strikers".
The organiser of the International Champions Cup says he understands Jose Mourinho's criticism of the pre-season competition.
"We play Real Madrid and we have no more players than what we have", Mourinho referred to United's tight squad in the US.
"I have learned nothing from this game", said Mourinho.
After an extravagant spending in the transfer market, Liverpool now have in their resources the most expensive goalkeeper and the most expensive defender in Alisson Becker and Virgil Van Dijk respectively. I think he was just voicing that frustration.