Mourinho has made it clear Rooney is his only transfer target this summer, but United are insistent the 27-year-old is not for sale.
There might have been a chance for Lampard and Rooney to discuss the prospect of becoming team-mates at club level when they were away with England before Wednesday's match against Scotland, but the Chelsea midfielder insists the topic never came up.
Yet there has been no avoiding the speculation linking Rooney with a move to Stamford Bridge.
"I think Chelsea have made their interest known. That's a decision for them and Wayne to come to," Lampard told Sky News.
When it was suggested to Lampard that Mourinho usually gets his way, Lampard agreed, saying: "Yes he does, I think that has shown, but when you're talking about us here we've got a big squad, we've got three or four strikers already.
"We're going into the season strong, but if the manager wants to add another player we all hope he gets his man."
Lampard is unwilling to speculate on whether Mourinho will have his wish to sign Rooney fulfilled.
"I'm really not sure. I don't know enough about it," he said.
"I didn't speak to Wayne about it when I was with England last week. He was training and he was focused.
Source: PA
Source: PA