Reality TV star Caitlyn Jenner's offer to be a "trans ambassador" to US Republican presidential hopeful Ted Cruz has drawn criticism from some members of the LGBT community, while major transgender rights organisations are staying out of the fray.

Jenner told gay and lesbian publication The Advocate in an interview posted this week that she admired Cruz despite the social conservative's stance on transgender issues.

The 66-year-old Olympic gold medallist-turned-television personality called Cruz a "great constitutionalist" and said she would like to advise him on questions relating to her community.

"Yes, trans ambassador to the president of the United States, so we can say, 'Ted, love what you're doing but here's what's going on'," Jenner, who last year became the most high-profile American to transition to a different gender, told The Advocate.

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The muted reaction to Jenner's support for Cruz appeared to show the high level of esteem she enjoys in the gay, lesbian, bisexual and transgender (LGBT) community. But that did not stop some of its members speaking out.

Zack Ford, the LGBT editor at ThinkProgress, a website affiliated with the left-leaning Center for American Progress, wrote in a post that Jenner's support for Republicans like Cruz tainted her "credibility".

Mara Keisling, executive director of the National Center for Transgender Equality, said Jenner's comments highlighted the fact a significant share of transgender people were Republicans.