The former champions have a new driver line-up this season, with 19-year-old British rookie Lando Norris and 24-year-old Spaniard Carlos Sainz, but have yet to name an official reserve.
Brazilian Sergio Sette Camara has been appointed as test and development driver but has yet to secure sufficient points to obtain the necessary super licence.
Double world champion Alonso, 37, left Formula One at the end of last season but is set to compete with McLaren at the Indianapolis 500 in May.
Season 2019
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Fernando Alonso

Image credit: Getty Images

Asked whether the Spaniard might be approached to step back into the F1 cockpit should the necessity arise, Brown indicated as much without giving a direct answer.
"Fernando's still part of the team with our Indy 500 project," he said.
I think we’d probably stop short of announcing a reserve driver, but I think there's a variety of drivers out there that if we need someone on short notice could fill that role,
McLaren needed a reserve in 2016 when Alonso was injured in the season-opening Australian Grand Prix and had to miss the following round in Bahrain with Belgian Stoffel Vandoorne stepping in.

Fernando Alonso

Image credit: Getty Images

Vandoorne is now competing in the all-electric Formula E series.
Brown had earlier played down media speculation that Alonso could take part in pre-season testing in Barcelona, without entirely ruling it out.
"Right now, we're taking testing one day at a time and focusing on our racing drivers," he said.
"I think any time you go into pre-season testing and are doing anything from reliability to performance, you kind of have a set plan but work at it one day at a time."
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Alonso to test for McLaren F1 team in ambassador role
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Season 2019
Ferrari unveil new Formula One car for new era
15/02/2019 AT 12:02