The Northern Irishman led Celtic to an unbeaten Scottish Premiership campaign - the first of any top-tier club since the late 19th century - claiming the title with a record-breaking 106 points.
Rodgers also guided the Scottish giants to the League Cup and Scottish Cup in his first season, sparking suggestions a return to the Premier League could be on the cards.
And skipper Brown insists he is not surprised by the interest surrounding Rodgers, despite him recently signing a contract extension to 2021.
“You never know as a player or a manager what is going to happen down the line,” the midfielder said to The Evening Times. “Real Madrid could come in for the gaffer over the next six months, you never know.
“You could probably understand teams would want him, the way we’ve been playing. Especially with what we did last year in winning the treble. You’d expect that, but for now he is signed up, and lucky enough for us we’re going to get four more years with him, hopefully.
"But he has signed up, he’s happy here and he’s enjoying it. He’s enjoying living in Bearsden and he’s enjoying his life. He’s the manager at a top-quality club.”
Brown also believes Rodgers' standing in England will prove beneficial to Celtic in the transfer market ahead of the 2017-18 campaign.
“As soon as people start talking about people leaving clubs in the [English] Premier League his name (Rodgers) gets mentioned,” he added. “I don’t think two or three years ago we’d have been able to touch anybody like that.
“But due to his name, and what he’s done in the game, he’s got a chance of bringing top-quality players to the club and that’s what he wants to do. He wants to maintain the level that we set last year but also push us on.
"It’s been a good year last season. We have an early start with the Champions League. It is always going to be hard going back in as you saw in the game the other day. But hopefully this season is going to be just as good."