Sanchez is expected to leave Arsenal in January if manager Arsene Wenger is able to find a replacement before deadline day.
If no replacement is found, Arsenal face selling Sanchez to either Manchester United and Manchester City or forcing him to stay until the end of his contract and losing him on a free transfer.
City are prepared to let United win the race for Sanchez due to an unwillingness to meet Arsenal’s £35million asking price.
Yesterday, United boss Jose Mourinho hailed Sanchez as “phenomenal” and refused to rule out a move for the 29-year-old.
But the situation has taken a fresh twist with the arrival of Sanchez’s family in the country.
According to Goal, Sanchez’s older brother Humberto landed at London Heathrow Airport on today with other members of the family.
The Arsenal forward was with his team-mates this morning at London Colney as they prepared for their clash with Bournemouth on Sunday.
Sanchez was all smiles as he interacted with the likes of Calum Chambers.
He was also pictured practising his dead-ball routine with Wenger watching on closely.
Speaking in his press conference, Wenger admitted he was more hopeful of keeping Mesut Ozil and Jack Wilshere over Sanchez.
He said: “It looks like Sanchez will not extend his contract, but we want to keep Jack and if we have an opportunity maybe to keep Ozil, the rebuild will be less deep than if all three left.”
Former player-turned pundit Craig Burley thinks Manchester United’s interest is no problem for Manchester City.
“It’s not a problem, it’s not a problem,” Burley said.
“The player decides. It’s not a problem, not an issue. It’s Arsenal’s problem now.
“Alexis Sanchez is well within his rights, as we know as players with contracts that are coming up or whatever, to sit tight.
“He sits tight until the summer and he gets the move he wants, as long as City still want him.
“One hundred per cent (I can understand why he would want to join City over United), 100 per cent.
“And I can also understand why, supposedly, Man City would put two fingers up at Arsenal for not selling him back in the summer when they wanted and now playing hard ball.
“So they are quite prepared to say we’ll wait until the summer even with an injured (Gabriel) Jesus.”