Ferrari are in advanced negotiations with Sainz for the Spaniard to replace Sebastian Vettel at the team for 2021.
Sky Sports understands that talks are at a detailed stage for the under-contract McLaren driver.
It is possible both teams could make announcements by the end of the week.
Vettel hasn't revealed his future plans, although it is unlikely that Ferrari's rivals Mercedes and Red Bull will look to sign the four-time world champion.
"I think there's a good chance Sebastian will step away from Formula 1," said Sky F1's Martin Brundle.
Sainz. 25, made his debut in F1 in 2015 alongside Max Verstappen at Toro Rosso but while the Dutchman earned a move to Red Bull the following season, Sainz had to bide his time before moving on.
He joined Renault in 2017 but enjoyed his best F1 season last year with McLaren – finishing sixth in the championship and securing a sensational first podium in Brazil.
He is now the favourite for one of the most coveted seats in motorsport. One Italian Formula One journalist in Italy stated the deal between Sainz and Ferrari had already been done.
“The engagement of Carlos Sainz and Ferrari is already done. Official announcement expected tomorrow,” Luigi Perna wrote.
"This is a really strange time in that driver contracts are coming to their end and teams are having to make decisions based on the future with no current season as an indicator," said Brundle. "They're working blind at the moment.
"This plays into the hands, to an extent, of young but well-experienced drivers. The new kids in town haven't had a chance to prove themselves as a Leclerc or [Max] Verstappen of the future, for example.
"I see a scenario which is Sainz to Ferrari, Ricciardo to McLaren, and then that leaves a seat at Renault that probably would be [Fernando] Alonso."
Ricciardo left Red Bull for Renault in 2018, although the French team have struggled to lead the midfield since the seven-time race-winner arrived.
Lando Norris is currently the other McLaren driver alongside Sainz.