The two-time world champion Spaniard has been linked with a return to F1 in recent weeks with Red Bull advisor Helmut Marko revealing that he had been informed by Alonso's agents that the Spaniard was "available" for 2020.
Brown confirmed that Alonso could race for another F1 team.
Alonso raced in Formula One from 2001 to 2017 and spent his last four seasons with McLaren. He has also raced in IndyCar for a McLaren affiliated team.
"Fernando remains an ambassador for us," he said. "We have a great relationship and we are talking to him about racing programmes with us that are not related to F1.
"But we are happy if he wants to return to F1 and, if we don't have a seat available, to race for another team. We’d support him to do that if he wants to do it."
