Ibrahimovic signed a one-year deal in July 2016 and scored 28 times in 46 games in all competitions for United before suffering knee-ligament damage in April in the Europa League win over Anderlecht.
"He wants more at football's highest level", said Mourinho.
"We had three players as you know, one defender, one midfielder and one attacking player but for this beginning of the season we lost important players too, we lost [Marcos] Rojo, [Ashley] Young, [Luke] Shaw, Zlatan, we lost players for injuries so I think between the players we lost and we got we are in a similar situation", he said. "It's not something urgent, that we are desperate to have it done or not done, I just think that he was very clear by showing what he did a year ago was not enough for him." said Jose. "It's not something urgent, that we are desperate to have it done or not done".
"We have a central midfielder and a striker, so obviously another player would be one coming from the sides, but we have players and if we can not strengthen then we have people we trust".
And during Mourinho's first pre-match press conference of the 2017/18 Premier League season, he explained where things now stood between Ibrahimovic and United.
Having added Romelu Lukaku, Victor Lindelof and Nemanja Matic to his squad, Mourinho is hoping United make at least one more signing before the window closes, with Gareth Bale, Ivan Perisic and Danny Rose among those linked with a move.
'Obviously [we wanted] a player for another position playing from the sides, but we have players and if you can not strengthen the team in these areas, we have people that we trust and we go for it'.
"I'm happy with the effort the club made and happy the club managed to do 75 per cent of the work before the Premier League starts". He has put his trust in me and in my work, and I was very grateful to him.
He said: "We have a giant on our chest which is really heavy, but we don't compare to the biggest clubs in Europe right now". Mourinho is a fantastic coach and won everything wherever he went.