Robson, England manager at the time, had dropped the mercurial Hoddle from the national side.
Brazil knew the legendary manager well during their time together at Ipswich, but came to blows over the midfielder.
Hoddle played his last game for England in 1988, when he was at Monaco, and Robson refused to bring him back in.
Brazil told talkSPORT: "I remember getting a right hander from Bobby Robson over you (Hoddle). I was on the train from Ipswich going to London.
"I was going to Heathrow to head to Australia to play out there for three or four games, but I ended up staying for four months.
"We were talking about you and I told him 'you've got to play him, boss'.
"He said: 'No, the game has changed'.
"I said: 'No, no, no - if he was a Platini or a European, he'd be first on the sheet'.
"We argued like mad. As we got near Liverpool Street, he said 'son, the game has changed. You've got to work harder and Glenn is so gifted but doesn't work hard enough. He won't play for me again'. And you didn't."
Hoddle, who joined talkSPORT on Thursday morning, added: "You could have told me! There was me out in Monaco sweating.
"I always felt when I went to England I was having to reprove myself. Back in the day, there wasn't a No.10 position in England.
"When I went to Monaco with Arsene Wenger, within a week there was a No.10 position for me and it was the most important position in the team. The players knew that, the manager did and the press too.
"But in England, it was 4-4-2 and we played in teams that changed from that with a diamond, but I never played there. Ricky (Villa) played in the 10."