Rodgers has been linked with Tottenham this week.
Dyer told The Sun: "Brendan Rodgers has done a great job and got the balance right.
"He's a fantastic coach, old school if you like, who explains himself and knows how to manage players and expectations.
"It's inevitable that someone is going to come calling for him at some point but I would be devastated if he leaves and so would the other players.
"It would be a massive setback if he decided to leave."