"I know Earl personally," Ball said after the Los Angeles Lakers' shootaround Wednesday morning. "I think he has coaching experience in the league. Obviously he went there, he's alumni, so I think he's a good fit."
UCLA, after a 15-point home loss to Liberty, fired Steve Alford on Monday. He coached the team for 5½ seasons, leading the team to four NCAA tournaments and three Sweet 16 appearances.
Watson, 39, played at UCLA from 1997 to 2001 and then in the NBA from 2001 to 2014.
"He's been in the league," Ball said. "He knows how to get to the league, how to stay in the league. He coached in the league. I think he's the best for the job."
Watson addressed potentially going back to coach his alma mater in March 2017 after Alford was rumored to be in line to become coach at Indiana.
"There's no doubt that I love my school," Watson said. "It took me out of a poverty situation and gave me hope. The school is an amazing place. I feel like it saved me. But I also feel like [former Memphis coach] Hubie Brown saved me in another way.
"Playing for the Utah Jazz, they were there during a difficult part of my personal life and they helped me a ton. And then, of course, the San Antonio Spurs, after the death of my brother, the love they gave me is what I needed most, and that love is genuine. So you have different points in your life where people and groups come into your life and none of them are family and they impact you for the positive."
Ball said Watson has had that type of impact on him, even though they played at UCLA nearly 20 years apart.
"I know he's in the practice facility all the time in the summer working with guys and helping teams out," Ball said. "I just know him personally off the court. He's helped me with a few things off the court businesswise. I think he's a good person for the job."
Ball played for Alford in his lone collegiate season (2016-17), averaging 14.6 points, 7.6 assists and 6.0 rebounds for the Bruins before being selected by the Lakers with the No. 2 pick in the 2017 draft.
"Steve Alford, he's a good person, good coach. He helped me a lot," Ball said. "I got a lot of love for him. It's tough, but he'll be all right."
Murry Bartow, who is serving as the Bruins' interim coach, said Wednesday he was caught off guard by Alford's firing.
"I was surprised at the timing of it. Look, I've been in coaching 30 years, so I'm not real surprised by anything, and that's not a coach's decision," Bartow told reporters. "That's an administrative decision. I didn't feel it coming, expect it coming. We were 7-6 and we've been struggling, but yeah, I was caught off guard a little bit."
ESPN's Kyle Bonagura contributed to this report.