Chelsea were often linked with Rice throughout Lampard's tenure and the former Blues boss has spoken about his admiration for the midfielder during a Q&A session for the Willow Foundation on Friday and said that the transfer didn't come off for "various reasons".
"We are fortunate to have him in England, West Ham are fortunate to have him. He's a leader and it is clear that he's destined for great things," said Lampard.
"I have probably given it away with how I spoke about him but I think it's common knowledge that I was a big fan of his.
"It didn't happen for various reasons, but we brought in a lot of players in the summer. But I was a big fan of him.
"For understandable reasons, West Ham know the player that they have on their hands.
"I don't want Declan to be in an uncomfortable position through this because all I see from him is absolute performance and desire to play for West Ham.
"They gave him the chance there and the choice will be Declan's as the years go ahead, but his performances are great to watch."