Martinez played for the Swans between 2003 and 2006, during which time they narrowly avoided being relegated from the Football League, gained promotion to League One and then moved from the Vetch Field to their current ground.
The Spaniard was the Welsh outfit's captain and in 2007 he came back to take over as manager, subsequently guiding them to the League One title in 2008.
A year later he moved to Wigan, where he stayed for four seasons before leaving over the summer to take up his current post with Everton.
He has already returned to Swansea on two occasions with the Latics, and ahead of this weekend's trip as Toffees boss, Martinez said: "It brings great emotions for me, because as you can imagine I have a very soft spot for Swansea - not just as a former manager, but as a former player and captain.
"To be a foreign player who was the captain of that club in such a specific period of their history was a memory that I will never forget."
Swansea have continued to go from strength to strength without Martinez, getting promoted to the Barclays Premier League in 2011, winning the Capital One Cup earlier this year and making it to the last 32 of the Europa League this term.
They have, though, continued to play the same sort of flowing football, with Paulo Sousa, then Brendan Rodgers and now Michael Laudrup in charge, that they did under Martinez - a style similar to that of his current Everton team.
Martinez insists "this match is not about managers", but added: "It is a very important one for both clubs - two teams with a very similar football philosophy.
"It is going to be real fight to control the football and a real test for us.
"I think what Swansea have achieved over the last 10 years is incredible and that they are just showing a real model of how to develop a way of playing and how to be successful with it.
"I know it is going to be really tough, but it is a game that we are looking forward to."
Although they did win 2-0 at home against Swansea in a League Cup tie, Martinez's Wigan failed to beat them in the four Premier League encounters between the clubs.
He may well fancy the chances of Everton bringing him a victory against the Swans on Sunday, though, given their respective form.
The Toffees have lost only once in the league all season and are unbeaten in nine matches, while their hosts have won just two of their last 12 games in all competitions.
Martinez feels the additional demand of a Europa League campaign is taking its toll on Swansea this term, but he is also in no doubt that the club are better for the experience overall.
"Everyone knows it is a physical demand, but also there is the mental fatigue - people are not used to it," Martinez said.
"You have to travel all over Europe, then come back and in around 48 hours you have to face another game in the league. Probably that drops your level a little bit.
"It is demanding to play European competitions, but I'm sure it has been a great experience and that the club will be better for it. So it has its pros and cons.
"Probably it has affected the amount of league points they have this season, but as a football club they are stronger than they were last season and I'm sure they are enjoying it and still being involved in it."
Everton have James McCarthy back available for this Premier League game, with the midfielder having completed his suspension for collecting five bookings this season.
On-loan Barcelona forward Gerard Deulofeu has been ruled out for between six and eight weeks with the hamstring injury he sustained against Fulham, and Tony Hibbert (knee) is not yet ready for first-team involvement again.
Fellow defender Leighton Baines is continuing to work his way back from a broken toe, with Boxing Day's home clash against Sunderland looking likely right now as the point at which he will be able to make his return to match action.