The "Bound 2" rapper sparked romance rumours with Bradley Cooper's model ex last month (Jun21) when they were seen at a hotel in France for his 44th birthday.
And while Kanye apparently invited Irina to go to Paris for a couture show with him, she is said to have declined.
"She likes him as a friend, but doesn't want a relationship with him," a source told the New York Post's Page Six. "She doesn't want the association that they are dating, which is what would have run in the press if she showed up (in Paris with him). It would have been another month of news saying that they are dating."
"She doesn't want to be linked with anyone right now. She is happy being single."
Kanye has a history with the Russian-born beauty - she appeared in his 2010 music video for "Power" and previously modelled for his Yeezy fashion line - while the hip-hop heavyweight also gave her a shout-out in his "Christian Dior Flow" track over a decade ago.
Kanye split from wife Kim Kardashian - the mother of his four children - earlier this year, and the pair are in the midst of obtaining a divorce.
Kanye and Kim married in 2014. They began dating in 2012 while she was still legally married to Kris Humphries. Kim and Kris split only 72 days after their lavish wedding. Kim filed for divorce while Kris requested an annulment. Their divorce was eventually finalized in 2013.