The 22-year-old is out of contract at the end of this season and it was reported on Thursday that the Toffees have had a fee worth up to Â£5million accepted by the Elland Road side.
Byram is a long-term option which could provide a short-term fix with Seamus Coleman out injured, but Martinez pointed out that any potential deal is still a long way off.
"There has been an approach
There is nothing else to comment on
You have to careful," he said
"From there to conclusive news is a long gap."
Coleman is expected to be out for another three weeks with a calf strain sustained in last week's Capital One Cup semi-final first-leg victory over Manchester City
The Toffees are light when it comes to cover for him at right-back, with Tyias Browning ruled out for the season with a knee injury and veteran Tony Hibbert's fitness issues mean he has not played a match in 13 months
John Stones filled the void in Wednesday's goalless draw at City, but ideally the Toffees want him operating in the centre of their defence.
When asked to discuss what qualities Byram has, Martinez said: "I wouldn't be that disrespectful to players registered to other clubs."
Martinez also offered an update on a possible departure for Steven Naismith, who has been linked to both Norwich and Swansea recently
"It is in his (Naismith's) hands to a point
It has to be right for everyone
We are open to Naismith's situation," he added
Source : PA