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Sanchez, 28, has just 12 months remaining on his current Arsenal contract and doubt has been cast upon his future.
Express Sport understands the Chile international has already rejected a new £300,000-a-week contract.
Manchester City are said to be keen to swoop with Pep Guardiola keen to secure a reunion with the forward.
But Arsene Wenger is determined for him to sign a new deal and to keep him at the Emirates.
Sanchez is currently on holiday after playing in the Confederations Cup while Arsenal are on their pre-season tour in Australia.
But Wenger outlined he has been sending texts to his prized asset in a bid to convince him to stay at the club.
“I have spoken through text and it was very positive,” Wenger said.
“My thoughts are always positive. There’s not a lot to resolve at the moment with the player.”
He added: “Players like Alexis Sanchez played the whole season, finished the season really tired and went off to play in the Confederations Cup.
“You can’t tell them they are not having a holiday and must come back and continue, it’s impossible.
“Usually you need three weeks but they will have a programme and can be involved after one week to ten days, and play a part in games.
“It also depends on the shape they come back in.”