Waghorn has just one game remaining in his loan deal and will return to Leicester City after the weekend's game with Blackburn Rovers.
"It goes without saying that I'd love to keep Waggy, but obviously that's down to the chief executive and chairman," Sky Sports News quotes Lomas as saying.
"He is in the prime of his career at 23 and is the type of player we want to keep around. I've told Waggy that we want to keep him.
"I want to take him full-time. That is the kind of deal we should be doing. He can play in various attacking roles - up front and out wide - so we would be mad not to want him."
Millwall are currently 17th in the Championship.