Shami Chakrabarti, who led an inquiry into anti-Semitism within Labour, has refused to say whether she has been offered a peerage by the party.
The former Liberty director, who is a Labour member, dodged questions about her political ambitions and whether Jeremy Corbyn had offered her a place in the Lords.
Her report, which concluded that Labour was “not overrun by anti-Semitism”, was labelled a “whitewash” by critics.
Appearing on Jewish TV channel J-TV, Ms Chakrabarti was pressed on her future within Labour.
She said she would “probably not” run as an MP, but repeatedly sidestepped questions about a peerage.
“I don’t know whether I want to talk about my future ambitions at this point,” she said, adding: “You can ask the question and I’m going to evade it at this point.”
Labour leader Mr Corbyn’s spokesman said: “We don’t comment on Labour Party nominations to public bodies or recommendations for political appointments.”
Ms Chakrabarti’s review recommended that Labour members should not use terms such as “Paki” or “Zio” and should steer clear of invoking Hitler, particularly in debates aboutIsrael and Palestine.
But it found that “the Labour Party is not overrun by anti-Semitism, Islamophobia, or other forms of racism”.
Board of Deputies president Jonathan Arkush said the report was “weak on the demonisation of Israel” and “omitted any mention of party figures who have displayed friendship towards terrorists”.
Jonathan Sacerdoti, director of communications at the Campaign Against Anti-Semitism, said the report was a “vague, meaningless whitewash that will do nothing to rid Labour of anti-Semitism or address the total absence of leadership it has shown on this issue”.
Tory MP James Cleverly said: “Always felt Shami had huge integrity, hope she didn’t pull her punches on Labour anti-Semitism report for a peerage.”