Reps for the 21-year-old told Mail Online that reports of a breakup were 'absolutely not true' and confirmed that the couple are still together.
The Bang Bang singer and her 25-year-old rapper beau first went public with their relationship in October and have been red carpet fixtures together since that time.
A report by Star magazine on Friday claimed that the Break Free singer allegedly found risque images on the rapper's phone last month.
An insider told the weekly: 'She refuses to return his calls. She feels completely violated and has lost all trust in him.'
Adding: 'His grandma passed away a few days later and she hasn’t even called to check up on him. They’re done!'
But a rep for Ariana told Mail Online that the reports have no basis and are 'absolutely' false.
It appears the couple spent Christmas Day apart, as Big Sean's grandmother died on December 23, according to his social media post, of which he added an Image and a tribute message:
'My grandma passed away a couple days ago. I haven't said anything to anyone because honestly I feel like she's still here.'
Meanwhile a day later on Christmas Eve, Ariana spent time with her family, including her grandmother and dogs, and shared the image with her social media followers, writing, 'Surprised nonna w/ a new friend & tiny companion... she named her noel.'
She also thanked her fans on New Year's Day via Twitter, writing: 'Hope i’m not too late to say this but just wanna thank you 1 more time from the bottom of my heart for making 2014 so special!! a dream. ily.
'Even tho there were some difficult moments i’m very appreciative of the love u continuously show. u make everything better :) really love u.'
And the year has been a boost for the beauty, who ended a string of gigs with a raunchy performance at Y100's Jingle Ball 2014 in Florida in December, and performed at the Victoria's Secret fashion show.
Previously Ariana dated The Janoskians rocker Jai Brooks on and off since 2012 and ended things ahead of meeting Big Sean in August of last year. And Big Sean was engaged to Glee actress Naya Rivera in October 2013, but ended the engagement April of last year.
