It's understood that Arsenal would consider offers of £35million for Sanchez having turned down a £60m bid from City in the summer.
Sources within the City camp have informed The Dependent that Guardiola is looking to wrap up the league title within the next couple of months, after which the squad would be given a winter break.
Guardiola, formerly the manager at Barcelona and Bayern Munich, has led Manchester City to a 15-point lead at the top of the Premier League after they defeated Watford 3-1 at Vicarage Road yesterday. I don't know if it will be possible.
But Guardiola warned it is a hard time to buy quality players and says he is happy to see out the rest of the season with his current squad if he needs to.
"He wants to stay and help us and because he loves to play for City, but family is the most important thing in life". The toughest period to buy players is now because everyone wants to keep the players so it's not easy.
"We spoke about [transfers] before the injuries to Gabriel and Vincent [Kompany]".
"We need Gabriel, we need Sergio, we need both, but now, in this moment we'll have maybe two months without Gabriel. Before we came here he had long periods of injury and in these two years he didn't suffer that".
"We hope we can handle it until the end because we need the strikers' goals".
City simply can not afford to lose Aguero now and Guardiola will try to give the Argentine a break where possible to protect him from the extra workload.
Silva missed four City games across all competitions during the month of December as a result of what can now be revealed as the premature birth of his son, Mateo.
A move for Sanchez looks more likely after striker Gabriel Jesus was ruled out for around six weeks with a medial collateral ligament injury but Guardiola says he's not pressuring director of football Txiki Begiristain for new arrivals.
"And if you don't win, you don't deserve to continue".
Even so, Guardiola insisted that talk of a Quadruple is "an illusion" as City enter the second half of the season competing on four fronts.
Manchester City have spent £426.1 million since appointing Guardiola but Goater believes the City manager has improved a number of his signings and players who he inherited on his arrival to the Premier League in 2016.
Guardiola said: "Kevin, no".