Speaking at the Final Four in Phoenix on Friday, Robertson told ESPN's Andy Katz that "I'm rooting for him" to break the record and that "I hope he does it."
"I always thought he was a great basketball player," Robertson said of Westbrook. "I was talking to some basketball people the other night, and I said, 'I don't think any of these guards can beat him in a one-on-one game.' I think he's been tremendous for the team, his fans and also for television."
Westbrook needs three triple-doubles to surpass the 41 that Robertson recorded with the Cincinnati Royals in 1961-62. He has seven games left in the regular season after Friday night's 100-95 loss to the San Antonio Spurs, in which he had 32 points, 15 rebounds and 12 assists.
Robertson also endorsed Westbrook as deserving of MVP honors for his season's accomplishments.
"I think it's Westbrook. That's what I really think," Robertson told Katz of his MVP pick. "Because years ago it was tough to win an MVP because it was based on winning championships, and [Bill] Russell with the Celtics -- they dominated. But one year, Wilt [Chamberlain] averaged 50 points a game and 29 rebounds and me a triple-double, but Bill won because his team advanced and we did not.
"It's changed now. A lot of people understand what an MVP means. They understand basketball better than they did years ago."
Westbrook was averaging 31.8 points, 10.6 rebounds and 10.4 assists per game this season entering Friday. He is on track to join Robertson as the only players to average a triple-double for a season. Robertson posted 30.8 points, 12.5 rebounds and 11.4 assists per game in that 1961-62 campaign. Westbrook had a 99.9 percent chance to finish the season averaging a triple-double, also entering Friday, according to ESPN's Kevin Pelton.
Information from ESPN's Royce Young contributed to this report.