José Mourinho has admitted re-signing Zlatan Ibrahimovic is an option, with the Manchester United manager also refusing to rule out a move for Chelsea’s Nemanja Matic.

Ibrahimovic is recovering from a serious knee injury at United’s Carrington training base and is a free agent after being released by the club in the close season. The Swede, 36 in October, was United’s top scorer last season with 28 goals. Of a new deal, Mourinho said: “Possible, it’s open. There was not a new contract [to allow] time for everybody to think, feel and decide. From his point of view he made the decision of wanting to play football still at the highest level. He didn’t want to hide behind such an amazing [serious] injury – it would be easy to hide behind it, stop and go to a different level of football.He made the challenge for himself to keep playing at the highest level.”

Mourinho added: “We open our door for him to recover with us, and at the same time let’s make a decision that makes us all happy. If that is for him to stay and for us to wait, let’s say, until December maybe, because I don’t think before December he can get back to competitive football. But why not wait for a player who gave us so much. We are changing ideas and it’s with Mr Woodward [executive vice-chairman] and Zlatan’s agent but the final decision is the best for the player.”

Mourinho wants a holding midfielder with Tottenham Hotspur’s Eric Dier a prime target. United have also been linked with a move for Matic, who appears set to leave Chelsea having been given permission by the Premier League champions to miss their tour of China and Singapore. However, it is believed Chelsea will resist letting the 28-year-old join United after they beat the London club to the signing of Romelu Lukaku.

Asked if he could kill the question of an interest in Matic, Mourinho did not. “I can’t say any word about a player who is a Chelsea player. It’s difficult, he said. We have to respect the player, the club, the owner, the manager. I don’t want to be disrespectful, we don’t have our door closed. We are not happy with just [Romelu] Lukaku and [Victor] Lindelof, we need more. We wanted four [in total], so I would say 50% of the job done.

“But I don’t want to say that because everything is so difficult. I would [not] like to be in Ed Woodward’s position negotiating because everything is really difficult. So maybe we don’t get two [more players], we get one. But we need one more to give us more options, we have players that belong to the squad but cannot play for next few months, [Marcus] Rojo, Ashley Young, Luke Shaw, if Zlatan stays [another]. We need two more players I would say, at least one. But I don’t want to say Matic or any other name because I don’t think it’s correct.”

Mourinho confirmed Real Madrid’s Alvaro Morata was the subject of a serious but ultimately failed bid. This suggests Lukaku, who was signed earlier this week for £75m, may not have been the manager’s first-choice.

“Yes, we have had interest [in Morata], that is obvious and it’s public,” said Mourinho. “We have not come to an economic agreement, that is obvious as well. But it’s Real Madrid’s right to ask for their players the amount of money that they want. We do not determine what the price is of a player of Real Madrid, Real Madrid do that. And we didn’t arrive at an agreement with Real Madrid.

“I do not criticise Madrid and I am not going to criticise my board because my board has made the offer, and they have tried to reach an agreement during a time, and they didn’t come to an agreement. It’s simple.”

Ragarding what Lukaku can bring, Mourinho said: “Hopefully goals. Everybody knows he’s a striker so we’re not speaking about a multi-functional player or [going to] create doubts about positions on the pitch, he’s a striker and normally strikers score goals.

“The reason why he was so important and difficult to get is what he did in the Premier League. Obviously there are other good strikers in football but the Premier League is a very specific habitat, a difficult habitat, normally they need some time to adapt and Lukaku plays in [the] Premier League for the last four or five seasons.”

He added: “Now he comes to a club with a different responsibility than Everton or West Bromwich Albion [two of his previous clubs], and he comes in the right moment because he is young but still years of experience within the Premier League and for the Belgian national team. It’s his first Champions League competition [next year] which was his main motivation so the fact we qualified also played an important role.

“For the characteristics of the Premier League we need a target man, which is not [Anthony] Martial, [Marcus] Rashford - the clear nine, the one that is comfortable to play in the box and the defensive line we thought Romelu would be a good option for us.”

Mourinho made a late intervention into Lukaku’s transfer. “I didn’t negotiate, it was Mr Woodward who negotiated with Romelu, his agent and the Everton board,” the 54-year-old said. “The only thing I did was to call him when the situation was almost there just to guarantee him that he would be an important player in my team.

“And it’s quite a great experience the fact we worked together already for a few months and during the time when I was at Chelsea. Our relationship was always very close despite it not working well for us together. He’s intelligent, he’s polite, we kept the contact, the feeling. Now we are back together in different moments and I have no doubts it is going to work.”

Ivan Perisic, the Internazionale forward who is another of Mourinho’s targets, may only be allowed to leave for United if the Italian club can take Martial on loan, it is understood.