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Leishman, 61, was diagnosed with a brain tumour in February last year and had surgery in March to have it removed.
The operation was successful but the cancer has returned. He is at home with family in the Auckland suburb of St Heliers.
A familiar television face since the early 1970s, Leishman's best known role was as host of game show Wheel of Fortune, but it is in the world of sports broadcasting where his legacy will be most keenly felt by friends who call him a "real gentleman".
He was the cherub-faced sports presenter who sat alongside such broadcasters as Dougal Stevenson and was named sports broadcaster of the year in 1978.
Racing was a big interest and he presented Turf Talk with Glyn Tucker until the show closed in 1979.
Leishman, who has three children with wife Michelle, had a television career over four decades, latterly as the host of the HSBC Golf Club.