The actor has spoken publicly about his love for the "Funny Girl" actress, and at the age of 14 wrote her a letter, inviting the star to stay at his home in Swaziland for a "two-week holiday, or longer," after reading she was "feeling very tired and pressurised" by her fame and failed romance with Ryan O'Neal.
Now 62, Grant is still a massive fan of the singer, having recently acquired a two-foot statue of the star, but he told the New York Post's gossip column Page Six his devotion to the hitmaker was once a worry.
"I was in psychoanalysis when I was 42 and I asked the shrink is this unusual to be a middle-aged person as I was then still having this mad obsession," he explained. "And he said, 'Well, it's probably arrested development at some level in adolescence' but he said as long as you're not hurting anyone and it makes your life tick along, then so be it."
When Grant published his fan letter to Streisand on Twitter last year, she responded, and the pair have met several times since.
"I was at a screening at Donna Karan's place in the East Hamptons while I was working in Philadelphia last summer and managed to have a two-hour one-to-one face-to-face with no interruption conversation with her 'til one o'clock in the morning with her. For a fan, that was about as good as it could possibly get," he gushed.
"I think she's extraordinarily beautiful, has the most amazing talent... Can be hilarious and heartbreaking in a heartbeat of each other."