Swinton, who won the best supporting actress Oscar for her role in the movie Michael Clayton, has two partners: John Byrne, 67, and Sandro Kopp, 29.
But website Live News reported Byrne - a director, artist and playwright - had been romantically linked to lighting director Jeanine Davis, 42, for two years.
Swinton, 47, has an open relationship with Bryne, and the actress also has a relationship with Kopp - a painter from Wellington.
Byrne told Live News the situation was "relaxed and amicable".
"We have not hidden away and Jeanine is very much part of my life. Tilda knows all about it and is more than happy with the situation.
"Tilda has Sandro and the arrangement works very well."
The unmarried couple live together in Scotland with their 10-year-old twin boys.
John also revealed to Britain's Daily Express that Davis had met his family and Tilda's other lover.
"I wouldn’t say we all socialised together but she has met Sandro and we have all been under one roof together ... I know some people will struggle to understand it, but it works for us.”
Swinton's relationships became public at the Oscars when a journalist asked her about her personal life.
"I don't have a husband, I've never been married," Swinton said at the time.
"I have children with someone else, with whom I'm bringing up my children, and I've lived with someone else, my sweetheart for the last three years, and maybe it's extraordinary that we're really all friends."
In 2001, Kopp's paintings of female genitalia were removed from the Wellington Autumn Home and Garden Show after complaints.
He had non-speaking parts in The Lord of the Rings and The Lion, the Witch and the Wardrobe. Swinton was the White Witch.