The Canterbury Labour MP received criticism from Labour activists and online abuse for the belief that it might not be suitable for trans people to have access to some single-sex spaces such as domestic violence refuges.
According to The Telegraph, one Tory MP has suggested the offer of moving to the Conservative Party could have been made through an intermediary.
The claims arose after it was alleged three Labour MPs were thinking about moving to the Tories.
However, according to The Times, Rosie Duffield has no urge to move to the Conservative party.
She said: “At times when abuse is really rife on social media, we do support each other and it’s really nice to get support from all colleagues in parliament, but I’m not about to jump ship.
“I’m Labour through and through.”
Rosie Duffield did not attend this year’s Labour Party conference in Brighton out of fear for her own security.
Sir Keir Starmer has publicly challenged Rosie Duffield’s argument of “only women having a cervix” by saying: “it is something that shouldn’t be said. It is not right.”
Speaker Sir Lindsay Hoyle has also spoken about the online abuse and condemned the threats against Ms Duffield.