The request was revealed in secret correspondence between WikiLeaks and Trump Jr.
"Please cease using Seth as a political football in predetermined partisan narratives," the family said.
Former intelligence contractor Winner was arrested after allegedly leaking documents about Russian attempts to hack the 2016 U.S. presidential election.
The Brexit campaigner is a "person of interest" for the FBI because of his links to Julian Assange and Russia.
The WikiLeaks founder will stay in the embassy until the U.K. clarifies whether it has received an extradition request from the U.S., his attorney tells Newsweek.
Activists argue that a danger to WikiLeaks "is a threat to all free journalism."
Assange's lawyer argues that because the U.S. has new plans to charge Assange, Sweden should drop its warrant.
The director, who won an Academy Award for a film about Edward Snowden, sees WikiLeaks founder Julian Assange as a historical figure.
Laura Poitras's Risk shows the WikiLeaks founder in all his anti-authoritarian glory, as well as illustrating his dodgy relations with women.
The former Republican congressman said the whistleblowing group is a tool used by Russian military intelligence.
Lenin Moreno is expected to extend government rule by winning Sunday's run-off vote against Guillermo Lasso.
WikiLeaks Editor Julian Assange was speaking at a press conference from London's Ecuadorian embassy.
Assange said last week he would accept extradition if former military intelligence analyst Chelsea Manning were freed and on Wednesday U.S. President Barack Obama commuted Manning's 35-year sentence.
More than 100,000 people signed an official White House petition urging Obama to pardon Manning before he steps down.
Trump says Assange is right, "Russians did not give him the info!"
Assange has spent four years living in the South American nation's embassy in London.