Pep Guardiola believes he may have to sign a defender in the January transfer window or Manchester City could be “in trouble”.

Benjamin Mendy is recovering from a serious knee problem and will not return before April while John Stones has a pulled hamstring and is unlikely to play before the new year. Guardiola also admits Vincent Kompany is too injury-prone to be relied on, the captain having to be replaced at half-time of the 2-1 win over Manchester United at Old Trafford owing to his latest muscle malady.

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“We are thinking about it,” Guardiola said. “In that department we have too few players and to handle all competitions we are in trouble, real trouble if this is the case. But I can’t assure anything. We’re going to see what will happen in January.

“Maybe we are thinking of looking at another central defender because of Vincent’s problems, John Stones is four or five weeks out. And we miss an important player like Mendy.”

Guardiola may again try to sign West Bromwich Albion’s Jonny Evans following last summer’s failed bid. He had to turn to Eliaquim Mangala as a 59th-minute replacement in the derby, Ilkay Gündogan having replaced Kompany at the interval.

Mangala was nearly sold in the summer but Guardiola may now have to use him more. “We were clear on Mangala that we needed a solution in the summer,” the manager said. “The moment we didn’t I met with him in my office and said: ‘Now you are my player, you’ll be treated like everyone else.’ The reason we looked for another one, he knows. But in some games he is going to help us.

“At half-time of the derby I didn’t use Mangala because I tried to send a message to the players that I wanted to win the game. After we scored, I thought Zlatan Ibrahimovic would come in, so I decided to put Mangala in front, and pulled a striker out [Gabriel Jesus] because I wanted one more man in the middle to make more passes.”

Guardiola has a contingency plan should Kevin De Bruyne or David Silva be injured. “They are so important players and if it does happen Gündogan will be ready, Phil Foden will be ready, Yaya Touré will be ready for us to find a solution.”

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Sunday’s derby victory was a fifth consecutive 2-1 scoreline for City. Guardiola praised the spirit of his side, who travel to Swansea on Wednesday evening, in being able to win while not always performing at their best.

“It’s a very healthy team spirit,” he said. “When you win a lot of games it helps you to build that spirit but the most important thing is the spirit wasn’t lost last season even though we were more sad, more upset because the results were not like we expect. It’s impossible to achieve [City’s record-equalling] 14 league wins in a row just by playing football. Forget it.

“The people outside the club can discuss many things but in games our spirit shows we were there to try to do our thing, like at Old Trafford, which is so demanding a stadium. Nobody can assure you, but my feeling is right now – I don’t know in the future – we are going to try to do that, play with spirit.”