According to The Express & Star, Villa are interested in signing Loftus-Cheek on loan from Premier League rivals Chelsea this summer.
The Daily Mail has claimed of interest in the 24-year-old from Southampton and West Ham.
Chelsea boss Lampard has said that the England international could go out loan this season to play regular first-team football.
Lampard told Chelsea’s official website about Loftus-Cheek: “I’m very open with Ruben and we’ve had a couple of conversations in the last week.