Arséne Wenger has admitted that Alexis Sánchez is “mentally and physically jaded” but insisted that he was pleased to see the Chilean visibly distressed after Arsenal’s 3-3 draw at Bournemouth because it shows a winning mentality.

Sánchez proved instrumental as Arsenal scored three late goals to come back from 3-0 down to claim an improbable point, yet at the final whistle the 28-year-old took off his gloves and hurled them to the ground in frustration in front of the travelling Arsenal support before marching off the field without shaking hands either with the Bournemouth players or the officials. Earlier in the match he had also engaged in an argument with his team-mate Aaron Ramsey.

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“I don’t look too much how people how they talk, I look how much they want to win,” said Wenger. “What is surprising there? You want to see that kind of passion. You don’t come down from 3-0 down from 70 minutes without that passion. We wanted to win the game and we didn’t and we’re all frustrated. Mentally and physically Sánchez is a bit jaded. You could see that he is tired. He can have sometimes emotional reactions but face to face he is always very respectful.”

Sánchez has 18 months remaining on his £130,000-a-week contract and negotiations are continuing about a more lucrative renewal, although his reaction at Bournemouth could suggest he is growing increasingly frustrated at the club. Wenger, however, said that Sánchez was “all right” in the dressing room after the Bournemouth draw.

“The other players care as much as he does, don’t worry,” Wenger continued. “Everybody has his way. There was no celebration in the dressing room; everybody was disappointed that they didn’t win the game. There is no hierarchy of intensity of desire to win at that level. Everybody wants to win.”

Sánchez played every minute of Arsenal’s festive fixtures and Wenger confirmed that he would be rested for Saturday’s FA Cup third-round trip to Preston. “He wants always to play. On one side when I don’t play him, people say: ‘Why don’t you play him?’ and on the other hand I am criticised for using him too much. But I always planned in my head, no matter what happens, in January he will need a breather.”

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Olivier Giroud is again expected to lead the line at Preston, and has scored in each of his last three games, but was criticised for elaborately celebrating his injury-time equaliser at Bournemouth when there were still four minutes remaining for Arsenal to score a winner. As some team-mates attempted to beckon Giroud back to the halfway line the Frenchman continued to celebrate, mimicking his scorpion-kick goal against Crystal Palace on New Year’s Day.

“Giroud is a winner. He is a fighter. I can understand Giroud. He thought the game was lost, it was 92 minutes. You score. You don’t lose. The 3-3, he gave two assists on the night. We can understand that but, ideally, you want not to waste time any more but he scores goal after goal and he scores important goals.”

Indeed, no forward in Europe’s top five leagues has a better record at present: Giroud has contributed either a goal or an assist every 49 minutes this season, seven minutes fewer than anybody else. In comparison, Lionel Messi has done the same once every 68 minutes.

Another attacking option for Wenger is Danny Welbeck, who could make his first Arsenal appearance since May at Preston after recovering from a severe knee injury. “Physically Welbeck’s fitness is at quite a good level, but of course the ideal way is to give him two or three games with the under-23s,” said Wenger. “But the situation is not always ideal, sometimes you have to hurry up.”

With Lucas Pérez struggling with an ankle injury sustained at Bournemouth and with Theo Walcott and Mesut Özil also sidelined, Welbeck could make his comeback from the bench at Deepdale.

Laurent Koscielny is another that will be rested because of “two problems in his thigh”, while another injury concern is Francis Coquelin, who had a scan on a hamstring strain on Thursday and is expected to be out for between three and four weeks.