Despite splashing out on Arsenal striker Robin van Persie, there has still been speculation that the Reds could be interested in adding another left-back or midfielder to the squad.
After being asked by MUTV if he is happy with his group going into the new season, the manager suggested that there is a mystery name still in his thoughts if a deal can be done.
"I think that is maybe it [in terms of signings this summer]," he conceded. "Maybe in one other position.
"We have spent a big amount of money and, if I need to go to the owners, I am sure they would say 'yes'. But it's only if a certain player would become available."