Daniel Ricciardo will depart the team at the end of 2020 to join McLaren, leaving an opening at the Enstone-based squad alongside Esteban Ocon.
Alonso won his two F1 world championships in 2005 and 2006 with Renault, however in recent years, it has been unable to challenge at the front of the grid and is still awaiting its first podium finish since returning as a works team in 2016.
Alonso's former boss Brown says that if he was running Renault, signing Alonso for 2021 would be his top priority.
“I spoke with him the other day, and was kind of poking around, and I think he’s undecided,” the American told Sky Sports F1.
“If I was running Renault, that’s who I’d put in the car. A big name. Fast as anyone. Won two championships with them, so he’s got history. So from a Renault perspective, I think he’s a bit of a no-brainer to put in.”
In his final years at McLaren, Alonso grew frustrated of competing in the midfield, which resulted in a number of team radio outbursts.
The 38-year-old said earlier this year that he was interested in a return to F1 in 2021, when the new technical regulations were set to come into play.
However, due to the coronavirus pandemic, the new rules have been set back by a year. And Brown doesn't believe that Alonso will want to commit himself to a team that is not yet capable of winning.
“Whether Fernando wants to get back to 22 races, with a car that doesn’t look like it’s capable of winning yet... I think given Fernando’s stature, what would get him to jump at a seat is if he thinks he could be on the top of the podium.
“So given that they’re on a similar kind of journey [as McLaren] back to the front – and I think they’ll get there, they’re a great team, great resources, great company who’s been there and done that before – I don’t know if Fernando has the appetite to be on a three-year journey versus getting in a car that he can win in in 2021.”
Bahrain International Circuit - Winter testing