Steve Bruce is eager to strengthen his defence and was hoping Holding would arrive on a season-long loan from the Emirates.
He allowed defender Florian Lejeune to join Spanish side Alaves on similar terms though Holding was persuaded to stay at Arsenal by Mikel Arteta.
The Gunners are willing to sell Chambers this summer and want around £12m for him but Newcastle would favour a loan deal.
Chambers had a temporary spell with Newcastle’s north-east rivals Middlesbrough four seasons ago so is no stranger to the area.
Though Gunners boss Arteta was not expecting any immediate departures from the Emirates when speaking earlier this week.
“I think every case you take it individually,” he said. “First of all try to understand if they want to leave, why.
“At the moment I’m not expecting anyone to leave shortly. We are trying all the time to adjust the squad in the most efficient way.
“It is clear at the moment that it has to go both ways and in order to achieve that we still have some time but we are pretty clear in what we are trying to do.
“Again, with all the players that we have here, we're going to try to get the best out of them.
Get the latest transfer news straight into your inbox!
Want to be on the ball with all of the latest football news?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
“We're going to try to improve them as much as we possibly can and create the right environment for them so that they are happy at the club, because I believe it's the most important thing for them to perform to the level that we want.
“After that, obviously in the market there are things that we cannot control. There are things that we can control and let's try to manage in the best possible way."