O'Ward enjoyed his first taste of F1 machinery at the end of last year in Abu Dhabi when he took part in the young driver test as a reward for scoring his maiden IndyCar win for the Arrow McLaren SP squad.
The Mexican driver finished the year third in the IndyCar standings and was in contention for the championship until the final race, taking wins in Texas and Detroit.
Following his test in the McLaren MCL35M in Abu Dhabi, O'Ward said he thought there was a two-year window to make an F1 switch happen, and that he would do "everything I can to make it happen".
McLaren Racing CEO Brown has long stressed the importance of O'Ward remaining focused on his duties in IndyCar, and felt that winning the championship would be the easiest way for him to stake a claim to a future F1 seat.
"That's exactly what I told him, the quickest way to F1 is to go and do what Juan Pablo Montoya or Alex Zanardi or Jacques Villeneuve or Michael Andretti did: go win in IndyCar," Brown said.
"That's going to be your best chance of getting into F1. He's unbelievably talented. He's a great personality. I think he's got what it takes from a raw talent point of view to be a Formula 1 driver.
"Obviously Formula 1 is a much more different discipline, so he's got a lot to learn, with all the buttons for example. But for sure he will [learn].
"He needs to stay very focused on IndyCar. It's going to be his best route into F1. I think his [two-year] timeline is about right."
The comparison to Montoya is one that Brown has previously bestowed on O'Ward.
The two drivers are set to be teammates for McLaren at this year's Indianapolis 500 when Montoya returns to the team in a third car for the race.
O'Ward scored another major career victory last weekend by winning the LMP2 class at the Daytona 24 Hours with DragonSpeed alongside Colton Herta, Devlin DeFrancesco and Eric Lux.
But he vented his frustration earlier this month over the "ridiculous" requirements of the FIA superlicence points system, which only rewards the IndyCar champion with the necessary 40 points to race in F1.
