Brown was at Hibernian in 2007 when a delegation of players went behind Collins' back while he was out of the country and complained to the Easter Road chairman, Rod Petrie, about their manager's training methods.
Deila is aware of the friction that episode created prior to Collins' eventual resignation several months later and has spoken at length with Brown, who is currently on holiday in Miami, about the history that exists between the midfielder and the newly-appointed assistant manager.
The Celtic manager has heard enough to assure him there will be no issues between the pair and the Norwegian has revealed too that he wants opposing views, outspoken opinions and a degree of creative tension to help him build the kind of club he desires.
"I asked him [Brown] about John, but, as he said, it has been many years now and he's a professional, a little older and maybe brighter as well," said Deila. "It's not going to be any problem and, of course, I'm the manager. It is Scott and me who are going to have the most important dialogue.
"I think this is a much bigger thing for you [the media] than for them. In football, you have seen fights, a lot of things, and this is not a thing at all. If there is no temperature, there is no development. If everyone goes to training and returns home and thinks, 'I don't give a s***', we will stay at the same level all the time.
"We need disagreement, but we have to solve it in a good way for Celtic and for the squad. I know that is going to be handled very well. People mature as well. Seven years ago, I couldn't have been standing here as Celtic manager. If they had something in the past, they are grown-up people and I know that is not going to cause any trouble. We need strong opinions and personalities.
"It was a telephone call I had with Scott because he is in Miami and that is a little bit too far to go. I've spoken with some of the players and, of course, Scott was one of them as he is the captain and a very important player for us."
Deila understands that Collins possesses very definite views on how a club should be run, with fitness and professionalism central to his philosophy, while he has a very particular outlook on the way the game ought to be played.
While agreeing broadly on the path they will follow to take Celtic forward, the Norwegian expects strong discussions behind the scenes and appears to be actively relishing that prospect. "When I spoke with John, I understood he was the right one," said the 38-year-old. "We started talking and didn't stop for a long while. I think we are going to have a lot of good discussions.
"I love strong people. You really get real fights and arguments and that will make me better and it will make him better. At heart, we agree on football and I also love the standard he has about professionalism. His experience from Europe is also important and he is curious to learn.
"It is important to have a Scottish person beside me as he knows the players and the league as well as knowing the club inside-out."
Deila has also confirmed that Brown will remain in situ as club captain for the campaign ahead. "You never say something is forever but of course Scott is going to be the captain," said the Celtic manager. "What I like about Scott is his professionalism. It is the same as John. They give 100% in every training session.
"On the pitch, when something is going wrong, Scott takes care of it and turns it around. That's what you need from a captain. Passion is everything and Scott brings that to the team. You need players who can turn things around when it
is going wrong. You need them
to be hard mentally. I have heard about his sense of humour too, but
I need to learn the language a little bit better first. For now, I will just laugh when the others laugh."
Ronald Koeman, who was appointed as the Southampton manager earlier this week,
is understood to have an interest
in signing his fellow Dutchman Virgil van Dijk from Celtic, but Deila hopes to persuade the centre-half to stay in Glasgow for his first season in charge. "The day something comes to the office and it is real, we can talk about it, but
I want to keep Virgil because he is a fantastic player," he said.
"He is a very important player
for us to go into the Champions League with. I will do everything
I can to keep him."
Deila is also talking to former Hearts goalkeeper Craig Gordon about a contract and insists there could be a place for him within
his squad even if Fraser Forster, who is at the World Cup as part
of the England squad, remains at Celtic Park.
"Of course they can be here together," said Deila. "Craig has been a fantastic keeper. If he can handle the training, there is a good goalkeeper there and everyone has seen that. The medical staff are saying he can handle the training now. That's important if he is going to go back to the same level, or maybe become even better."
Deila, however, has cooled speculation that he will return
to his former club Stromsgodset
as he makes his initial moves in the transfer market. "You need the Champions League standard and Norway is far away from that,"
he added. "I hope we can get some Scottish players. That is the best thing."