Monk, unbeaten since taking charge of the Swans following the sacking of Michael Laudrup, takes his squad to Goodison Park to face Martinez's Everton side.
Monk played alongside Martinez at Swansea after joining from Southampton in 2004, and became Martinez's captain when the Spaniard returned as manager in 2007, despite missing almost the whole of the previous season through injury.
Martinez has gone on to manage Wigan and Everton, and has the Toffees firmly in the mix for Champions League qualification in his first season in charge.
The 40-year-old has been in touch with Monk following his shock promotion, and the Swans boss readily acknowledges Martinez has been a big influence on him.
"He was my captain when I first came here and I got to form a really good bond with him," he said.
"He was a fantastic leader and he came back as manager.
"I have learnt from him and the experiences he had here, it's like what I am doing now, taking charge after being a player and changing your role.
"He is a great guy and he is at the top of his game. Everyone always said he was an up-and-coming manager and I have experienced his management so we all know how good he is.
"He is probably even better now and it will be good to see his staff too, guys like Graeme Jones who was a really important part of our progression.
"You have to take the good bits from your managers and most of what Roberto and Graeme did was very good.
"We keep in contact, he texted me when I got the job and we have spoken since and I am sure we will have a good chat before and after the game on Sunday. That relationship will always be there no matter what."
Swansea's main focus remains Premier League survival, with the Welsh club four points clear of the drop zone after the midweek draw at Stoke.
But Monk is eager for more cup success, having tasted Capital One Cup glory last season, and still views the FA Cup as one of the highlights of the domestic calendar despite the tournament's fading importance in recent years.
"Of course we want to progress," he said.
"We had a good experience in a cup competition last year, and we'll be trying to win the game.
"If we can come through this game and the rest of the month with some good performances and good results, then I think it will stand us in good stead for the rest of the season.
"But we have to approach it how we want to and do the best we can."
He added: "If you speak to the foreign players it is one of the competitions they know best growing up, it is one of the biggest domestic cup competitions in the world.
"Football cultures round the world know about it so I don't think you have to promote it as much as people may imagine. They understand what the FA Cup is and they want to experience it."