The 95-year-old monarch was spotted heading towards the Duke of Sussex shortly after entering his British residence near Windsor Castle on Wednesday.
Harry, who arrived in the UK alone on Wednesday, will attend the unveiling of the statue of his late mother, Princess Diana, at Kensington Palace on Thursday July 1.
The monarch is said to be keen to talk to his grandson and act as a “peacemaker” following the recent crisis within the family.
The Queen’s decision is considered very crucial in the current situation. No sooner had Harry been driven from Heathrow to Frogmore Cottage when the Queen was stepping down. They would have plenty to say to each other.
Some royal watchers are now anticipating Harry’s meeting with Prince William. The two brothers have had a strained relationship in recent years, made worse by appearances by Harry in television interviews where he and Meghan Markle took aim at allegations against the royal family.
Meghan Markle has not joined her husband for the trip and will be staying at home to care for their two-year-old son Archie Harrison and newborn daughter Lilibet.
Prince Harry, who landed at the Heathrow terminal on Wednesday, will be quarantined for five days before being allowed to attend the event next week.