After the Portuguese coach's first spell at Stamford Bridge ended in 2007, Mourinho joined the Italian side the following year.
"I tried to take him to Inter, but I was saying, 'You belong to Chelsea and you should stay'," Mourinho told reporters.
"I wanted to bring him but I also wanted him to stay. I told him, 'If you want to come I want you', but in the end he did what he wanted to do and signed a new contract at Chelsea.
"He was not very far away, but in the end I was happy and I told him so. It was a good decision."
Lampard joined Chelsea from West Ham United in 2001.