The pair are former team-mates, while the two clubs will be chasing a spot in the last eight of the competition when they take to the field at Goodison Park at lunchtime.
Monk recently replaced Michael Laudrup, who was surprisingly sacked at the Liberty Stadium following a slump in form.
Martinez is a former manager and skipper of Swansea and last season led Wigan to FA Cup glory at Wembley.
Monk said: "He was my captain when I first came here and I got to form a really good bond with him.
"He was a fantastic leader and he came back as manager when I was captain.
"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 were 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."