The Blues have had two bids for the unsettled forward rejected by David Moyes's side, who insist that the England international is not for sale.
Rooney appeared as a second-half substitute for the Premier League champions in their 4-1 win at Swansea City on Saturday but Lampard remains keen to see his side's interest pursued.
|4/1||Frank Lampard is 4/1 with Bet365 to be Chelsea's top Premier League goalscorer
"I think Chelsea have made their interest known. That's a decision for them and Wayne to come to. We're going into the season strong but, if the manager wants to add another player, we all hope he gets his man."
Lampard and Rooney both featured for England on Wednesday as the Three Lions beat Scotland 3-2 in a friendly at Wembley but the Blues hero insists that he did not discuss any potential transfer with the United man.
"I didn't speak to Wayne about it when I was with England last week. He was training and he was focused," the 35-year-old added.
"I'm not privy to transfer stuff. That's for clubs to decide. I'm a player. I just keep my mouth shut and train and play."