Speaking after United's 2-0 pre-season win over Manchester Cit in Houston, Mourinho told the gathered media, "When I look to the team and when I look to Lukaku, Lindelof, I would like my squad to be here, my whole squad.
"If you manage to get one more player, I am not even crying for two, but if we can get one player as soon as possible because you can see the way Lindelof and Lukaku are in the team, with the understanding of the players," he added.
The United boss recently suggested that he felt the club was half way to finishing their intended summer business after the arrivals of Lindelof and Lukaku, but even just one more new signing might now be sufficient ahead of the upcoming campaign.
United remain linked with Inter winger Ivan Perisic and could still be in the market for a defensive midfielder, but any deals are in the hands of executive vice chairman Ed Woodward and Mourinho admitted all he can do is wait.
And as for any new players arriving before United finish the American leg of their tour next Wednesday after further games against Real Madrid and Barcelona, Mourinho said he is powerless and just hopeful.
"I am not in control of that. The credit of Lukaku and Lindelof to be here on time, the credit is not mine, it is Ed Woodward and his team. I thank him for that fantastic work to bring us two very important players for us," the Portuguese explained.
"But we need a bit more when you see the other teams in the Premier League, like Man City, Liverpool and West Ham, the way they get players, good players, important players. The champions have bought three fantastic experienced players.
"I am thinking about West Ham for the first match of the Premier League. They have got Joe Hart, Chicharito and Arnautovic. It looks like they are playing to win the Premier League too. The teams are fantastic in the market. I am waiting for a bit more."