The former Arsenal and England forward took the reins as Reds coach in early June when Aron Winter was sacked and although he won just four of 24 matches, Koevermans is confident he should remain in the role.
"I think he's the good man here to try to do it next season," said the Dutchman.
"For me personally there was progress here because we did better by the formation we had. When you look at the last  games without a win you would say 'No,' but I think when Paul came in we improved and you can say because of too many injuries we couldn't hold onto it.
"So I truly believe that we were better when Paul took over."
Koevermans added: "I'm pretty confident [Mariner's the right coach].
"He gave me the confidence I needed. He's just a genuine guy. I like him. He's a good coach. What you see is what you get. With his appearance on the [side]line, how he works with us, he's basically almost in the field and he wants to kick the ball in himself."