The pair played together at Swansea, before Martinez took the job as manager in a tenure that saw him name Monk as captain, and the Everton boss hopes his successes continue.
“The job he is doing is terrific – and I am not surprised," Martinez said, speaking to the South Wales Evening Post.
"I thought the biggest decision was the way he assembled the squad in the summer. When I arrived at Swansea, we had the clear idea that Garry had to be the club captain and we built the squad around him."
"He has that personal knowledge of what Swansea City should be and the decisions he has made early on in the season have allowed him to start so well."
“But it’s never been a question of whether Garry could be a great leader or someone with great football ideas."
"I respect him a lot and, as you can imagine, I have a soft spot for him, so I hope everything goes well for him this season.”
Despite the high praise for the Swansea manager, Martinez was disappointed with the result as he watched his side lose their second game in three days following the 3-2 home loss against Crystal Palace on Sunday.
“We are disappointed with the result, but not with the performance."
"We started really well, we stopped Swansea from being their normal selves and playing their normal controlling football. Considering the changes we made, I thought the performance was very, very good.