Paris Saint-Germain sporting director Patrick Kluivert is also keen on the Chilean, but fears that City, Manchester United and Chelsea may beat them to his signing.
Sanchez, who has 22 goals in most competitions this year, played the full 90 minutes as Arsenal stolen to your risky 3-0 defeat to Crystal Palace on Monday.
In his column for the Standard, the 70-year-old delivered a scathing verdict of the Arsenal squad.
Despite heading into the final year of his contract, the Gunners are reluctant to part with their star man and could demand £40 million for him.
Sanchez played under City boss Pep Guardiola at Barcelona and the 28-year-old 108-cap worldwide has grown increasingly frustrated in north London this season.
Arsenal boss Arsene Wenger refused to confirm Alexis Sanchez has been offered a new £300,000-per-week contract but stressed the importance of keeping the wage bill sustainable.
Reports yesterday suggested that Manchester City were 'very close' to agreeing a deal to sign Alexis Sánchez, with the attacking deciding that a move to the Etihad Stadium would be his preference.
"Some people tell me: 'Just give him what he wants.' But then you can not respect any more any wage structure and you put the club in trouble as well".
The Frenchman earns around £290,000 a week and with a proper rebuilding job expected to take place at Arsenal over the summer, they need their best players to stay at the club.
White did admit, however, that he thinks Sanchez will still leave, despite the huge offer that has been made to him by the Gunners.
"We've got aims we want to meet this season, there is still lots for us to play for".
"Sergio is more of a striker but Alexis can play there - from the start of the season he has played really, really well", he said.