Kanye West & Irina Shayk Still Together Despite 'Cooling Off' Rumors

Kanye West and Irina Shayk are very much in a relationship despite reports to the contrary, and rumors she turned down an overseas trip with him are nonsense ... TMZ has learned.

Sources close to the couple tell us they're still dating, just as they have been for months, and recently spent the Fourth of July weekend together in San Francisco -- and not in hiding either. We're told the couple dined out together at the fancy restaurant, Mourad.

Afterward, Kanye took off to Paris for the Balenciaga show during Fashion Week. Page Six reported he wanted Irina to go with him but she declined -- however, our sources say that's not true. We're told Ye hadn't invited her because it was a quick business trip, he flew in and out of Paris the same day.

The Irina-free trip sparked speculation their relationship was "cooling off" -- but we're told things are as hot as ever.

As we first told you ... the musician and supermodel have been together for months, though word of their relationship didn't break until after they hung out in France for his 44th birthday, and hopped on a private jet back to the States together.