Mike replied: “I do but I have loads of regrets about not asking her so many more things and having nervousness when you get that lucky seat to sit next to her.”
He went on to say he wish he would have asked her about history.
During her 70 year reign, the Queen saw 15 Prime Ministers and met 13 out of the 14 American presidents.
He added: “I was starting to get to that point but I hadn’t barrelled in – I know you would have barrelled in.
“But guaranteed, when you sit there, it’s not that easy.”
Mike and Zara Tindall married in 2011 and have three children – Mia, Lena, and Lucas.
In the podcast, Mike also opened up about how the Royal Family dealt with the death of Her Majesty.
He said the past few weeks have been “emotional but happy” and in “some ways amazing” to see the family come closer together.
He added: “You never predict it. A 96-year-old lady, you know it’s going to happen but you’re never ready for when it does.
“Watching what Zara had to go through, obviously she loved the Queen beyond everything else. Their connection with horses, they had a real bond around that.
“It’s like the world has lost its grandmother in some way.”
The Princess Royal chose not to give Zara and her brother Peter Phillips royal titles when they were born.
Anne previously said she thought it would be “easier” for her children to go through life without HRH titles.
Instead, Zara has gone on to become an accomplished olympian in equestrian.
Source: EXPRESS CO UK