Athletic Bilbao coach Jose Angel Ziganda does not know if Kepa travelled to Real Madrid for a medical, but confirmed he did not have permission to do so.
Madrid reportedly want Kepa to boost their goalkeeping options, with the 23-year-old out of contract at the end of the season.
Athletic have warned Kepa — out of action for the last month with a toe injury — he will have to pay his €20 million release fee in full if he wants to join Madrid during the January transfer window.
"I have no idea if he did a medical, I don't know what to tell you," Ziganda told reporters on Friday.
"Kepa was at [the club's training ground] Lezama yesterday following his recovery programme along with [defender Mikel] Balenziaga.
"He didn't go to San Mames. I don't have any knowledge of a medical, no idea."
Asked to clarify whether Kepa had been given permission to have a medical at Madrid, Ziganda added: "Of course he didn't.
"He looks fine to me, he's the same as he always is, conversations are as normal and nothing has changed. The team is focused on Alaves.
"All the distractions from outside don't help, but in my case it's easy to ignore because these are external matters and the sooner they stop the better. When he has something to say, he'll say it.
"Kepa on Tuesday made an attempt of one step further to train but has relapsed and is uncomfortable. I hope that he will be incorporated with the group in the coming week."