The Everton boss is set to assume the reigns at Old Trafford at the end of the season, taking over from Sir Alex 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, emphasising that, as a manager, you cannot be daunted by your role.
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"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 have 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 did, however, note that Sir Alex 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," he observed. "I've seen some statistics and in the first six years he won 43 per cent 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."