The 28-year-old is said to have walked out of training mid-session one day last week before being involved in an angry confrontation with team-mates.
He was left out of the starting line-up for the match at Anfield, coming on at half-time with his team 2-0 down
He had a hand in the Gunners' goal, providing the pass for Danny Welbeck to score.
The Chilean has been linked with a move away from the club this summer, with some reports suggesting he could be tempted by the huge wages on offer in China, while French giants Paris St Germain are also reported to be interested.
Asked after the game whether his decision to leave Sanchez out of the starting line-up had backfired, Arsenal manager Arsene Wenger told BT Sport: ''Yes , but I felt that in the first half that the strikers suffered because we didn't dominate in the midfield and in the second half half you could see that it was easier because Danny Welbeck and Olivier Giroud were much better
So it's always debatable."
The Sanchez bust-up was widely reported on Monday morning and Wenger is sure to face questions about that - and his own future - during a lunchtime press conference to preview Tuesday night's match against Bayern Munich.
Arsenal are on the verge of Champions League elimination, having lost the first leg to the German side 5-1.
Former Arsenal striker Ian Wright, working as a pundit for BT Sport on Saturday, says he expects Sanchez's agent will now be trying to get his client away from north London.
"Our best player has been dropped today and came on and proved he shouldn't have been," Wright said on BT Sport.
Asked if he would stay in Sanchez's shoes, Wright said: " I wouldn't, simply because if I can't get in Arsenal's team when they're coming to places like Anfield when you need to win to try and stay in the top four and there's unrest around him anyway, why do I want to stay?
"We're not actually challenging for anything, we got hammered out of the Champions League
"He is a sought-after player and if I'm sitting in the dressing room like Alexis Sanchez today, his agent his probably making phone calls now!"
Source : PA