The England international signed a one-year contract extension towards the end of last season with the Blues, but this came after months of speculation surrounding the midfielder's future.
Lampard was linked with a move to the MLS as well as Manchester United, but Mourinho insists that he advised the 35-year-old to stay where he is.
"At that time [last season] I was not in contact with the club," Mourinho told Sky Sports News. "I was only in contact with him as a friend because we kept contact all over these years.
"I was telling him, the way I know you - don't go to American soccer. You are a player who needs to compete every week at the highest level, you are a player that needs to be in real competition. If you go to the States, it's a fantastic country, football is coming up and you would be very important there. But if you go there you will not enjoy your life, and you have years to enjoy your life as a player.
"So my opinion was not to go but try and stay at Chelsea - if Chelsea doesn't want you then try and stay in the Premier League because you belong to high level competition. He was telling me in the Premier League he doesn't want to play in any other club."
Lampard joined Chelsea in 2001.