“Irina is so upset at the lies about her and Kanye [cooling off]," a source tells PEOPLE about the couple

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Kanye West and Irina Shayk are still an item — and Shayk is not happy with the "lies" that they're heading toward a split.

Weeks after the couple made a romantic trip to France and days after Page Six reported that the two were breaking up, a source tells PEOPLE that West, 44, and Shayk, 35, are still together.

"Irina is so upset at the lies about her and Kanye," the source tells PEOPLE, adding that the model was moved to take legal action to set the record straight.

Of the rumors that "they're cooling off and she turned down his invitation to Paris," the source explains: "That's just not true. Kanye went to Paris for the Balenciaga show to support Demna [Gvasalia]. He was in and out, only there for 3 hours."

"They are very much still dating," the insider adds. Shayk and West recently spent time together in San Francisco — where he's currently working — for the Fourth of July weekend.

Last month, a source told PEOPLE that the two would "date long-distance" after spending time together in France.

irina shayk and kanye west
Credit: Taylor HIll/Wiriemage; Danielle Venturelli/Wireimage

"Kanye is doing well. He had a great trip to France with Irina. They will date long distance," a separate source said then. "Kanye will continue to be L.A.-based. He has no plans to move to NYC."

"He is very focused on business in LA too. He likes spending time with Irina though and plans to see her soon again," the source added.

Kanye West; Irina Shayk
Credit: Paul Morigi/WireImage; Michael Loccisano/Getty Images

West and Shayk were spotted together celebrating his 44th birthday at Villa La Coste in France in early June with a separate source saying he had "started pursuing her a few weeks ago" and that they had "hung out" in New York City, where she lives, before then.

"She seems smitten. He invited her to France and she happily accepted," the second source said at the time. "They are not officially dating, but there is an interest from both sides." The then-couple had spent three days in Europe before flying to the United States.

The romance between Shayk and West comes nearly five months after West's ex-wife Kim Kardashian filed for divorce from the rapper. (Kardashian aware of the brief romance and it didn't "bother Kim that Kanye is dating," according to a source.)

Kardashian and West share daughters North, 8, and Chicago, 3, and sons Saint, 5, and Psalm, 2. Meanwhile, Shayk shares daughter Lea De Seine, 3½, with ex Bradley Cooper.