The Anfield manager compares the incoming Red Devils boss' task in following Sir Alex Ferguson to his own in succeeding Kenny Dalglish and offers advice to his fellow coach.
The Everton boss is set to assume the reigns at Old Trafford on July 1, taking over from Ferguson as the veteran manager brings an end to his 26-year stay at the club.
Rodgers compares the task that Moyes faces in following the club legend to that which faced him when he took control following Kenny Dalglish's departure at Anfield, emphasizing that, as a manager, you cannot be daunted by your role.
"You have to respect the great past, and when I came in after Kenny Dalglish, I said it was a competition I could never win! This is a guy who was voted the greatest player in the club's history and has done so many great things on and off the pitch, so he rightly gets that iconic status," Rodgers told reporters. "But I wasn't daunted by the task of replacing a club legend. I didn't become a manager at 35 because I was shy. I arrived here with 20 years of work - it wasn't just presented to me. Kenny was an incredible man and David going in after Sir Alex Ferguson will be the same.
"David will come in and look to impose his personality, and it will take time because of the number of years his predecessor was there. But you have got to be strong enough to come in and at least know at the end of it all you've done it the way you wanted to do it."
Rodgers noted that Ferguson was not entirely successful in the early years of his reign, suggesting that the board should afford Moyes the same amount of leniency over the next few years.
"Fergie was given great support in those early years," Rodgers said. "I've seen some statistics and in the first six years he won 43 percent of the games.
"That is a great mark of the people and the board, and that's why I have great respect for the board here, because they really want to build something."