It is understood Cardiff owner Vincent Tan has told Bluebirds manager Malky Mackay - the man that guided them to the 2012 League Cup final, the Championship title last term and their current position of 15th place in the Barclays Premier League - to resign or face being sacked.
And asked if he could ever envisage receiving a message like that from Kenwright, Martinez said on Friday: "No.
"I think it is fair to say that that relationship is the most important one in a football club.
"I cannot comment about other clubs, because I don't know the ins and the outs, but probably that makes me even more satisfied with what we have at our club.
"I have been very, very impressed with our chairman and I don't think he has been getting the credit he deserves over the years.
"All I have had from him is support."
Kenwright became Everton chairman in 2004, since when the club, in all but two seasons, have secured top-seven finishes in the Premier League under the management of David Moyes, who was succeeded by Martinez over the summer.
The Spaniard added: "I think the manager's position can be a lonely place and you need the support from upstairs, that is clear.
"I'm delighted that at Everton, we have that in abundance."
Kenwright has come in for criticism from some Everton fans, with key concerns being the Toffees' relatively tight budget and the fact a new buyer has not been found for the club.
On the subject of finances, Martinez - whose fifth-placed side have lost only once in the league all season - said: "With the finances we have, what we have to do is use them well and be creative with it, and I have no problems whatsoever with that.
"I can tell you that the chairman and the board are always supportive and always want to find a way to allow me to do things with the playing staff.
"I couldn't be happier with what we have behind the scenes and the fans should know that.
"Sometimes it is all too easy to blame the finances when things are not going too well."
Looking ahead to the forthcoming winter transfer window, Martinez has already indicated he may delve into the market as he bids to find replacements for the likes of midfielder Darron Gibson and forward Arouna Kone, who are both sidelined by long-term injuries.
On Friday he also refused to speculate about reports linking him with a loan move for Manchester United winger Wilfried Zaha.
Martinez then said he had not had any approaches for striker Nikica Jelavic or defender Johnny Heitinga.
The pair have been left out of the Toffees first XI for most of the season, but Martinez said: "They are two players with incredible experience and they have been very important day-to-day.
"I can understand their frustration and down to the respect for what they have done I will always be helpful and try to understand their position.
"They are full internationals and looking to get to the World Cup, so you understand they have to play minutes, but in many ways I would love for them to stay here and play their role as they have been doing until now."
Martinez was speaking at his press conference to preview Sunday's league trip to his former club Swansea.
Everton have James McCarthy back available, 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 with Sunderland looking likely right now as the point at which he will be able to make his return to match action.
Baines trained this week and Martinez said: "We are going to assess how he responds to it.
''I expect Leighton to be available probably, if it is not this weekend, then the week after.
''It is just measuring well that we don't rush him back too early. But I would say he is not too far away, which is a beautiful Christmas present as you can imagine.
''If he has no reaction, he will be available to play on the Boxing Day, or possibly even earlier. But it just depends on how the next two days show up in his foot.''