Arbeloa fell back on an unwritten rule he said he learned the moment he first walked into the Real Madrid dressing room more than two decades ago.
Marca had broken the story earlier in the week that Ceballos confronted Arbeloa directly in his office at Valdebebas, informing the head coach that he wanted no further contact with him between now and the end of the season.
Ceballos is understood to have then told teammates about the exchange. The 29-year-old has made only five appearances totalling 144 minutes this season and has not featured since the squad that faced Real Betis last weekend, from which he was conspicuously absent.
The first question at Saturday's press conference went straight to the heart of it. Arbeloa's response was brief and practised.
"I don't get into public debates about situations with my players. The first thing I learned when I came here 20 years ago is that what happens in the Real Madrid dressing room stays in the Real Madrid dressing room. I have held that view for 20 years and I will keep doing so."
He was asked whether he had grown disillusioned with a group that has underperformed heavily across the season.
"Of course not, I defend them publicly. I'm in their hands because of what they show me every day. That's what a coach should do. We've had a pretty open relationship with most of them. Whatever needs to be resolved is between us. I will always defend them from this position."
He was pushed on whether the noise around the club — the Ceballos situation, the links to Mourinho as his replacement, the broader sense of a dressing room fracturing — was affecting his preparation.
"No, I'm focused on the next game and the noise doesn't bother me. I understand all the questions you have to ask. But my answer will remain the same. What I'm concerned about is the game tomorrow and the three points, which for me is what is important — for my team, the players, the club. That's the way I understand it."
Arbeloa did acknowledge that the team's collective output has been well below the standard the club demands.
"The results are far from what Real Madrid should be. You can't beat anyone these days just by getting off the bus. We have to improve a lot, collectively. The talent we have isn't enough to just keep the ball on the ground and play individually. We need a plan, a structure, a way to break down the opposition. It requires a different mindset and we've paid for it with points."
Real Madrid face Espanyol on Sunday evening at the RCDE Stadium, where Arbeloa is bracing for a hostile reception.
"I expect a match with two teams that need to win, for different reasons. Espanyol's stadium is always a tough place, with a great atmosphere and a fantastic coach. What I have seen from Espanyol this season has impressed me greatly and I have a lot of respect for what we will face tomorrow."