Daenerys may have crossed the Narrow Sea with the intent of saving the people of Westeros from a world of tyranny, but by the end of Sunday night's episode she was ready to see it all burn to the ground after Cersei executed her close friend Missandei. It's enough to make anyone noticeably worried, but what are Tyrion and Varys planning on Game of Thrones? They both seem to be starting to fear that their queen may not be the ruler the Seven Kingdoms need after all, though Tyrion is trying his best to remain loyal to his Dragon Queen despite the little slivers of doubt that keep creeping into his mind.
In the aftermath of the Battle of Winterfell in "The Last of the Starks," Dany noticed how the people love and admire Jon. And she suspected that if they were to find out he has a rightful claim to the Iron Throne, they'd want him to rule instead of her. She begged Jon not to tell anyone about his true parentage, because even if he doesn't want to rule, just having the information out there could ruin things for Dany. At the very least, though, Jon wanted to tell his sisters and naively thought it wouldn't make a difference. But, of course, it did. Sansa broke her word to Jon and told his secret to Tyrion, who in turn told Varys and brought about a rather treasonous conversation about who they would rather see sit on the throne.
For his part, Tyrion still wants to believe the best in Daenerys and seems determined to defend her. However, Varys is becoming much more wary and fearful that the Mad King's daughter could be following in his footsteps. After losing Rhaegal so suddenly, Dany was ready to burn King's Landing to the ground out of anger, regardless of the fact that it would kill millions of innocent people. Varys made it clear to Dany from the get-go that he serves the realm (aka the people) above all else and warned her that she was about to make a terrible mistake. She held off for the time being, but with the recent death of Missandei, it seems unlikely Dany will heed that advice now.
If that becomes the case, Varys may end up betraying Daenerys in some way. He wouldn't go back to serving Cersei, but he could attempt to set things in motion to make Jon the more desirable candidate to rule. Dany warned Varys that if he ever betrayed her, she would burn him to death. If she were to follow through on that threat, it may be the push Tyrion needs to alter his alliance for good.
During their discussion, Varys asked Tyrion who he felt would be the better ruler, Jon or Dany, and Tyrion was careful to side-step the question, saying that Jon doesn't want the throne so it doesn't really matter. But that in itself is an answer. He knows his queen has some dark impulses and if he were to see Varys burn before his very eyes, it could be what finally convinces him to rally to Jon's side.
At this time, Tyrion and Varys don't appear to have an actual plan in motion to betray Dany... yet. But that initial discussion could very easily lead to much more if the Mother of Dragons transforms into the Mad Queen.