"We definitely still have a strong and contractual relationship with Fernando," he added.
On her Twitter feed, Jenna Fryer - the journalist who initially reported Brown's comments - also posted a further statement from McLaren clarifying the position between the team and Alonso.
She tweeted: "Nothing whatsoever has changed in the relationship," the statement read. "McLaren and Fernando have a continuing and contractual relationship.
"Fernando remains a McLaren Ambassador [for McLaren]. No decision has been taken by McLaren or Fernando on returning to the Indy 500 at this time."
Alonso left the McLaren F1 team at the end of 2018 after a frustrating period where the squad was never in contention for victories. Instead, he found contention in endurance racing with back-to-back wins in the Le Mans 24 Hours race.
Alonso himself has suggested that now his WEC commitments have concluded, he's keen on moving on and undertaking an even bigger motor racing challenge - such as the Dakar Rally.
"Everyone said last year that I would not leave if I had a competitive car," he said of his decision to leave the Toyota LMP1 team. "But now I'm leaving a competitive car that is first and second in each race."
Plans for Alonso to take part in the Dakar in a partnership with Toyota have been described as 'very advanced' by Autosport magazine.
But one thing is for sure: the chances of Alonso ever returning to F1 appears to be receding all the time - even at a top team such as Ferrari, should an opening become available in the next year.
"I would return if I wanted to," Alonso told media in Spain this week. "But unlike the Dakar or another category, I have nothing to prove in F1.
"I retired with 21-0 [perfect qualifying record] over a teammate, which has never happened before.
"I didn't leave for competitiveness, but for the things, I like to do or," he added. "To take impossible challenges that I try to make possible."