The pair, whose romance was first reported earlier this month, were apparently staying at a mutual friend's house in London last night to avoid attracting publicity.
"Harry saw how tough it was for his brother William and Kate when they first started seeing each other," a source said.
"He knows the enormous interest in them drove them apart at one point so he really doesn't want that to happen to him and Mollie.
"They have both decided to take things easy and not put pressure on their relationship. They want to carry on seeing each other but will only do so inside the private homes of a very few close friends who they trust."