The ambulance was spotted on Thursday afternoon local time in the area near where Meghan and Harry live.
It comes as mystery surrounds details of the birth with the couple set to keep some aspects private.
BBC news presenter Simon McCoy tweeted: “Private ambulance with police escort seen driving through Windsor #justsaying.”
There has been a flurry of betting on names for the baby. William Hill was offering 4/1 on Diana, with Allegra and Grace at 8/1.
The bookies have stopped taking bets on the gender, which was widely predicted to be a girl.
It comes as news of Prince Harry’s plan to visit the Netherlands next week left royal fans convinced that Meghan had already given birth.
However, The Sun is reporting that the Duchess is yet to deliver her first born, a palace source has confirmed.
The source told Fabulous Digital that Meghan has “categorically not given birth” meaning that fans are still in for a wait for Baby Sussex.
The royal baby tradition Meghan Markle is breaking1:25
The birth of a new royal is one of their biggest events. However, with the imminent arrival of Baby Sussex, Meghan Markle has gone against many traditions.
Social media has been in a frenzy since the Duchess of Sussex’s reported due date in April came and went.
And Wednesday’s announcement that the Duke of Sussex is going on a royal visit to the Netherlands further fuelled their speculation.
Harry, 34, will launch the one year countdown to the Invictus Games on the overseas trip next Thursday — baffling royal watchers as they expected news of Baby Sussex’s arrival to be announced any day now.
But many have suggested he wouldn’t leave the country while his wife could go into labour at any moment.
This is being taken as proof that not only is the baby here, but he or she is a few weeks old because he wouldn’t leave Meghan, 37, alone with a newborn.
However, it seems that Harry could be at risk of doing exactly that following the confirmation that Meghan is still pregnant.
The arrival of the latest royal addition will be a private affair.
In a statement last month, the palace said: “The Duke and Duchess of Sussex are very grateful for the goodwill they have received from people throughout the United Kingdom and around the world as they prepare to welcome their baby.
“Their Royal Highness’s have taken a personal decision to keep the plans around the arrival of their baby private.
“The Duke and Duchess look forward to sharing the exciting news with everyone once they have had an opportunity to celebrate privately as a new family.”
Earlier this week The Sun reported how royal fans have accused the couple of “teasing” the birth on Instagram — begging the couple not to post until they announce the birth.
And The Sun also reported that the palace has shut down claims Meghan will unveil Baby Sussex on the cover of Vogue.
— with The Sun