The politically conservative Trump has taken a stance against marriage rights for LGBT couples, but Takei says he is confident that he can persuade his former Apprentice boss to switch his position.
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"He's a very fair-minded, decent man and I'm hopeful - and I'm an optimist - that being the decent man that he is, he will see [my view]," Takei told TV Guide.
Takei - who married his husband Brad Altman in 2008 - went on to suggest that Trump could help facilitate real social change if he agrees to support same-sex marriage.
"He certainly has a sphere of influence and [can] help create that climate where we become a better and truer democracy," Takei said.
Takei recently slammed his former Celebrity Apprentice co-star Clay Aiken, who he has described as "catty".
The Celebrity Apprentice airs Sundays at 9/8c on NBC.
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