In his podcast Tindall stated on Wednesday: "It's been a good week for me, had a little scan last week - third Tindall on its way."
The couple already have two daughters, Mia, 6, and 2-year-old Lena.
Speaking on The Good, The Bad & The Rugby, Tindall said: "I'd like a boy this time, I've got two girls, I would like a boy. I'll love it whether a boy or a girl - but please be a boy."
In what some may see as a slightly off-colour joke, Tindall added: "We're not sure what to do; Covi or Covina - I don't know where to go with names."
Tindall said his wife - who was the first member of the royal family to speak openly about miscarriage after she lost two babies following the birth of Mia in 2014 - was being cautious, but was in good health.
"Z is very good, always careful because of things that have happened in the past, and really looking forward to it," he said.
Zara, 39, spoke about her miscarriages in an interview in July 2018, revealing she had suffered a second loss before the birth of her youngest, Lena. She said at the time: "I think you need to go through a period where you don't talk about it because it's too raw. But, as with everything, time's a great healer."
Speaking of her first miscarriage Zara said: "In our case, it was something that was really rare; it was nature saying, 'This one's not right.' I had to go through having the baby because it was so far along."
Meghan Markle last month spoke out about her own miscarriage.
The Duchess of Sussex, also 39, wrote of the moment she knew she was "losing" her second baby in an essay for the New York Times.
She said she had decided to speak out about her loss because miscarriage was still a taboo subject which led to a "cycle of solitary mourning".
Asked about the baby's due date Tindall, a member of the England squad which won the 2003 Rugby World Cup, remained tight lipped, replying: "We like to play our cards close to the chest."
However, he admitted his eldest child has not been told the good news: "We haven't told Mia yet because we knew she would tell everyone at school, now that we've gone through the scan, yes [of]course we'll tell her.
"She'll be happy about it, she's been requesting another sister or brother, so we've hopefully fulfilled that role for her. She just wants something different now, Lena's growing up she's two-and-a-half now, she wants something younger to play with and dress up."
