"What I'd say is that there's so much opportunity to do good with a platform like that - and I think Meghan can maximise her impact for others, as well her own happiness, if she's doing something that resonates with her personally", she added.
However, the palace, which typically does not respond to speculative stories, denied that the argument had taken place.
Another article in the Daily Telegraph dished on Kate being reduced to tears during a dress fitting for Princess Charlotte before Meghan's wedding, allegedly over the way Meghan acted leading up to the wedding, which upset Kate.
"This never happened", a Kensington Palace spokesman said.
The royal family is officially getting into the holiday spirit.
Prince Harry confirmed he was dating Meghan Markle in November 2016, and a year later the couple announced their engagement.
Since then, Kate, 36, and Meghan, 37, have made several joint appearances as part of the Royal Fab Four - and even attended Wimbledon for solo outing without their husbands over the summer.
Meghan Markle and Prince Harry are scheduled to move out the Kensington Palace in early 2019, relocating to the grounds of Windsor Castle.
Additionally, during her visit with William to Leicester University on Wednesday, Kate didn't hesitate when she was asked by a fan if she was excited about Harry and Meghan's baby on the way.
She said: "Yes absolutely, no it's such a special time to have all kiddies. So it will be really special".
"Harry will want to establish himself and come out of the shadows and not be in his brother's shadows", one insider recently told PEOPLE.
The report also claims Kate, William and their three children George, Charlotte and Louis will be spending Christmas with her family at Bucklebury this year after the alleged row.
It's understood William voiced his concern to the Queen and his brother ahead of the royal wedding in May, the Mail on Sunday reported.
According to People, the two women will spend Christmas together amid all the feud rumors.