US Edition Asked by a little girl in the crowd whether she was hoping for a boy or a girl during a royal walkabout in Cumbria, the Queen replied: "I don't think I mind but I would very much like it to arrive because I'm going on holiday soon!"
The monarch added that there was "No sign yet" that the baby was about to arrive.
The Queen heads to Balmoral for her annual summer break at the end of next week, giving the Duchess another eight days to give birth before the Queen will be forced to decide whether to postpone her break.
Babies are normally induced once they get to two weeks overdue, meaning the Duchess could keep the world waiting until the end of July or even early August.
The Queen & The Princess Royal on a visit to Lake Windermere (Photo: Alamy)
The Queen is on a one-day visit to the Lake District with the Princess Royal, beginning her day in Kendal where they spent 20 minutes talking to local schoolchildren.
Eight-year-old Harry Coward, from Vicarage Park Primary School, and Amelia Nicholl, nine, from Stramongate Primary School, both in Kendal, gave the Queen yellow, lilac, green and red roses and sweet peas.
Harry said: "I gave her flowers. She wanted to know how much longer until the summer holidays. I think it was cool."
Mike Poole, headteacher of Stramongate Primary School, said: "The Queen was very interested and she mentioned how many local schoolchildren turned out.
"Kendal has done us proud today. It's been fabulous, the atmosphere."
The Queen and the Princess were presented with a hamper showcasing local produce by Tracey Graham, retail manager of Made In Cumbria.
Ms Graham said: "She chatted for ages. She was thrilled with the damson gin and said she would be keeping that for herself."
The royal party were also due to tour the James Cropper paper mill at Burneside Mill in Kendal, before taking a boat trip on Lake Windermere.
Meanwhile the Duchess of Cornwall celebrated her 66th birthday in Lostwithiel, Cornwall, where she was given a birthday cake by the local mayor, Gill Parsons. The Duchess cut the hat-shaped cake with a ceremonial sword, before the Prince of Wales joined well-wishers in a chorus of Happy Birthday.
The Duchess said earlier in the week that the Royal family were "waiting at the end of a telephone" for news of the royal baby and hoped it would arrive "by the end of the week".