The actress also met the Prince’s niece, Princess Charlotte, during the trip to Kensington Palace, Mail Online reports.
Kate was ‘really looking forward’ to meeting Miss Markle and added that the meeting was very ‘important’ to Harry.
The insider said: ‘They are very close and he really values her opinion on girlfriends.
‘Obviously Harry’s mother, Princess Diana, died when he was very young so Kate really fulfils that older sister/maternal role. It went really well.’
The couple have just returned from their first romantic holiday together in Norway, where they reportedly watched the Northern Lights.
With a month to go until Valentine’s Day, the Prince Harry is now said to be planning their second romantic getaway – a trip to Verbier, his favourite Swiss ski resort.
Sources at the resort told the Daily Mail that Royal aides have already carried out a recce to check potential security issues.
Miss Markle met Prince William two months ago at Kensington Palace while Kate was in Norfolk.
The time the 35-year-old has spent at the palace is seen as a sign of how serious relationship has become.
It should be recalled that Meghan Markle’s half-brother was arrested and charged with holding a gun to his girlfriend’s head on Thursday night.