City are prepared to offer more than ?35m for for the Chilean, who is being courted by a number of Europe's leading clubs.
The final fee could be as high as ?44m, which would make Sanchez the second most expensive player to be bought by a Premier League club.
On the move: Sanchez (left) looks set to leave Udinese but could yet join Esteban Cambiasso (right) at Inter
City officials are understood to have had positive talks with representatives of the 22-year-old over the weekend.
Since shining at last year's World Cup, Sanchez has attracted interested from Europe's biggest clubs. with Chelsea and Manchester United also believed to be monitoring his situation.
Should City be successful in their pursuit of Sanchez, he would replace Mario Balotelli with the unsettled striker likely to return to Italy with AC Milan one possible destination.
But City would have to take a significant loss on the ?24m they paid for Balotelli for that deal to take place.
World beater: Sanchez shone during the World Cup in South Africa
Members of Roberto Mancini's coaching staff have watched Sanchez several times, as has football administrator Brian Marwood.
City have also been linked with a move for veteran AC Milan midfielder Clarence Seedorf.
Discussions have taken place to explore the possibility of bringing Seedorf, 35, to Eastlands in the belief that City will be playing in the Champions League for the first time next season.
Seedorf said: 'I am hearing a lot of rumours,' he said. 'But I am awaiting an offer from Milan as there are some concrete offers on the table from Brazil and other clubs. But I will firstly think about the Scudetto before my future.'
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Source: Daily Mail
Source: Daily Mail