Villa are eager to cut short the season-long deal with Elliott failing to convince manager Unai Emery.
With the midfielder having already played for Liverpool and Villa this season, FIFA rules prevent him from joining a third team this season.
Aldridge says Elliott should be taken back by Liverpool, writing in his column for the Liverpool Echo: "It’s a no-brainer with Harvey Elliott. He’s not playing at Aston Villa so bring him back. The crowd love him.
"At his age, he’s more of an impact player. When he comes on, he does well. It’s a waste of a talent at Villa.
"We need numbers. We need players who can change a game and he can change a game. It’s a no-brainer.
"If Arne (Slot) doesn’t fancy him, he doesn’t come into the equation. But personally I think it’s a no-brainer to get him back into the squad for what he would bring to us - especially when we need more numbers."