It also bears remembering all the way back in season one, Grand Master Pycelle hinted at Varys' penchant for using poison.
When Ned Stark declared poison was a "woman's weapon", Pycelle responds: "Yes, women, cravens — and eunuchs."
So, before his execution, was he trying to have Dany killed?
Here's the exchange between Varys and the young girl:
Varys: "Nothing?"
Girl: "She won't eat."
Varys: "We'll try again at supper."
Girl: "I think they're watching me."
Varys: "Who?"
Girl: "Her soldiers."
Varys: "Of course they are. That's their job. What have I told you, Martha?"
Girl: "The bigger the risk, the bigger the reward."
Varys: "Go on. They'll be missing you in the kitchen."
The use of the phrases "try again" and the fear of being "watched" by soldiers really raises suspicions.
At first glance, it seems Varys may be referring to attempts to get the Queen to eat something for her own health. But given all that we know, it's also highly possible he wanted her to eat so she would fall victim to poisoned food — planted in front of her by the young kitchen maid.
If that was his intention, we now know Varys was unsuccessful — Dany heard about his secret support of Jon and had him roasted by one of her dragons.