When the Dutchman took over the Blaugrana he was tasked with overhauling an ageing squad.
Suarez, Ivan Rakitic, and Arturo Vidal were all allowed to leave for very small fees, with the club eager to get their wages off the books to allow for reinvestment.
The Uruguayan has since revealed that he was forced to train alone in his final days with the club, and that the treatment from Barca left him crying for days in his home.
However, Koeman now insists that if Suarez really wanted to stay, he could have, to try and prove his head coach wrong about whether he could still perform at the highest of levels.
"In the case of Suarez, it had become very difficult for him to start playing and I made that known to him. He found it difficult, but I never had any trouble with him at all," the former Netherlands boss told NOS.
"He trained normally, trained well. He finally made the choice to leave and I said: 'If you don't leave, for whatever reason, then you are just one of the group, then you can prove that I was wrong'. He could have stayed, yes.
"I'm good with Luis, but the club felt that we had to rejuvenate. You can see that now in the team. Ansu Fati plays, he is 17 years old. We have Pedri, 17 years old, who gets his chances.
Ronald Araujo is there at the age of 21. Trincao falls in a lot and is 20 years old, and we have taken Sergino Dest, who is 19. Those are all players for the future."
Koeman says he does understand the Argentine's point of view, but that it was ultimately the decision of the club.
"If you have someone in the locker room with whom you and your wife and children also hang out outside football, then such a reaction makes sense," he explained.
"I also said that to Messi: 'I understand that you are disappointed and think it is a terrible shame that he is leaving, but these are choices of the club'."
The Catalan side have started the 2020/21 La Liga campaign in solid fashion with wins over Villarreal and Celta before drawing 0-0 away at Sevilla.