Alexis Sánchez stormed out of an Arsenal training session last week and was involved in a dressing-room slanging match with some of his team-mates – which was, seemingly, part of the reason why Arsène Wenger dropped him from the starting XI at Liverpool on Saturday.

The Chile forward, who is Arsenal’s undoubted star, has cut an increasingly agitated figure over recent weeks as the club’s hopes of success in the Premier League and Champions League have fizzled out. His emotions bubbled over during the preparations for the league visit to Anfield.

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Sánchez stunned his team-mates by walking out of the session and, when they returned to the changing rooms to find him, there were angry words between some of them and him. The flashpoint is believed to have kicked off after an incident with another player.

Sánchez, who joined Arsenal from Barcelona in 2014, is stalling on signing a new contract at the club. The 28‑year‑old’s deal expires in the summer of 2018 and there are fears that he could try to force a move at the end of the season. The training‑ground bust-up will do nothing to counter the impression that Sánchez has had enough at Arsenal. Several leading clubs are monitoring his situation – chief among them are Paris Saint-Germain and Juventus.

Wenger told his players on Saturday morning the lineup for the Liverpool game and, after the 3-1 defeat, in which Sánchez came on at half-time and laid on the goal for Danny Welbeck that made the score 2-1, the manager said the player’s omission had been on tactical grounds.

Wenger said that he wanted to utilise the aerial threat of Oliver Giroud and Welbeck and play a direct game up to them – in order to get past the Liverpool press. But during a disastrous first half, there was little evidence of the tactic. Sánchez did inspire something of an upturn in the performance levels in the second half but it was not enough to avoid a defeat that left Arsenal outside the top four.

The situation with Sánchez represents the latest dark cloud for Arsenal. The club have lost four of their past six matches in all competitions – including the 5-1 defeat at Bayern Munich in the first leg of the Champions League last-16 tie. The second leg is at the Emirates Stadium on Tuesday night.

The future of Mesut Özil, who is widely considered to be the team’s other world‑class player, is in doubt. Like Sánchez, he will have only 12 months to run on his contract in the summer and is also nowhere near to agreeing to fresh terms. Özil was unavailable at Anfield with flu but he has been badly off-colour when he has played of late.

Then, there is the ongoing soap opera over whether Wenger will sign up for another cycle at the club that he has managed since 1996; his contract is set to expire at the end of the season. There is the offer of a new, two-year deal on the table and the hierarchy are desperate for him to stay – not only because of the levels of certainty that he provides but because they do not believe there is an outstanding candidate on the market to replace him.

Sánchez has been stroppy on the field in recent months, having argued, at times, with some of his team-mates. After the 3-3 draw at Bournemouth on 3 January, he threw his gloves on to the floor and stormed off down the tunnel. His occasional tantrums have been held up as evidence of his ferocious will to win and that is admired by many people at Arsenal. But, in these edgy and uncertain times, there is the feeling in some quarters that he is not helping the team’s situation.

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Wenger was ridiculed for the decision to drop Sánchez, who has scored 17 league goals this season – and 20 overall – and he said that it was not one he took lightly. He added, after the game, that it was one he was prepared to stand by.

“I don’t deny Alexis Sánchez is a great player,” Wenger said. “A decision like that is not easy to make. You have to stand up for it. I wanted to play two players who were strong in the air and then bring Sánchez on in the second half.”