Brown also believes that there could be more "fireworks" in the Ferrari camp involving Vettel and Charles Leclerc when this season's action finally gets under way.
Brown says he knew over the winter that there was a chance that Sainz could leave at the end of this year, and that he was in contact with Ferrari.
He had thus already lined up Ricciardo, who came close to joining the Woking team for 2019.
"Obviously Seb's an awesome driver and a four-time champion," he told Sky F1. "But I think we were pretty far down the path in the off-season, and knew we would either land with Daniel or Carlos.
"We never really entertained anyone beyond that, and especially with Seb's late breaking news - we were pretty far down the path at that point."
Brown revealed that he knew Sainz was eyeing a Ferrari opportunity, and confirmed that the Spaniard was given permission to talk to the Italian team, despite having a year of his contract to run.
"I've come to learn in F1 don't expect anything except for the unexpected," he said. "We had a sense, we started talking to Carlos in the off-season about his future with us and whether he wanted to drive for McLaren or Ferrari.
"We've got a very strong, open relationship with Carlos, his management and his father.
"This didn't come as a surprise, given how quickly we announced Daniel, and how quickly Carlos announced what he was doing. We were very joined up through this entire process.
"I think these movements would have probably happened with or without COVID because we started these conversations pre-COVID."
Brown expects there to be a continuation of the tension seen at rivals Ferrari last season.
"Clearly it's not a nice environment inside the Ferrari garage at the moment with the drivers and management, it seems to not be a happy family at the moment.
"Which I think is going to make for some pretty exciting racing in 2020 because I think we saw in Brazil the fireworks that were inevitable and building up. I'm anticipating more of that this year."
Brown says Renault is an option for Vettel, but believes he may be more likely to retire.
"It really depends, if Seb looks around, it doesn't look like there's a Mercedes or Red Bull opportunity for him, there's not a McLaren opportunity for him, clearly not at Ferrari, so the next best is Renault.
"And the next question is does Seb want to go with a team that is probably not going to win in 2021?
"It's a great team and they too should be moving up the grid but I think unless Seb wants to restart a journey with a team that's back on a journey - then I think he'll end up probably leaving the sport, unfortunately."