The troubled actor is currently in the middle of a dispute with network chiefs, who have scrapped the remainder of the eighth season of the hit show after Sheen went public with his criticisms of series creator Chuck Lorre last week (ends27Feb11).
The future of the show remains in jeopardy, with Sheen demanding to be paid $3 million (£1.8 million) per episode to return to work.
CBS President Les Moonves has since spoken out about the situation, admitting, "Going down the road... I don't know what's going to happen. I hope it's back. We'll see."
And now Weinstein has urged Sheen to make a deal to resume his duties on the family show.
He tells CNN chat show host Piers Morgan, "I worked with Charlie Sheen, he is one of the best actors when motivated. You see performances in Wall Street or Platoon, in our case he did Scary Movie and he sent up his own image.
"It's hard to judge but he's got a great family with Martin Sheen and Emilio Estevez and I hope the family and everybody rallies around him and they come up with a good decision.
"I know Les Moonves... Charlie's playing a losing game. Les is maverick in this situation, he's holding the parts. I trust Les to make the right decision (about the future of show). He's cool, he's smart."
Weinstein has also publicly backed the actor, insisting he'd employ him on a future project: "I'd hire Charlie Sheen to do Scary Movie 4, 5, 6, 7."
Sheen prompted the show's initial hiatus after he was hospitalised with a reported hernia following a wild night of partying at his Hollywood home in January (11) and subsequently sought professional help.