Suarez, 33, joined Atletico Madrid last month having become Barca's third all-time top scorer with 198 goals during a six-year spell at Camp Nou.
The Uruguayan striker's departure was sold as a cost-cutting measure as Barca looked to reduce their wage bill to minimise the financial damage caused by the coronavirus pandemic.
"There are a lot of contradictions [in Barcelona's version of events]," Suarez told ESPN's "90 Minutos" on Friday. "I would have looked for a solution if it was a financial problem and if it was a sporting issue I could have understood. It is not clear to me why they took the decision they took.
"I think they wanted to remove me from Messi's side. Maybe it annoyed them that I had a good relationship with Leo. Perhaps they didn't want him to be with me so much. I can't find any reason to think that would damage the team, though.
"We looked for each other constantly on the pitch, but for the good of the team. Maybe they wanted him to play with more teammates. That could have something to do with it. I can't find any other reason to want to separate us because we got on well on the pitch."
Suarez's departure came at the end of a hectic summer at Barcelona in which Messi had earlier tried to leave the club, only to be prevented from doing so in the end.
"They should have respected his decision to leave," Suarez said.
Messi's contract expires in 2021 but despite his desire to quit Barca last month, Suarez thinks his old teammate may extend his 20-year stay in Catalonia with a new president to be elected before the end of the season. Most of Messi's criticism of the club over the last month has been linked to current president Josep Maria Bartomeu.
"Leo's aware of what he means to Barcelona," he said. "He's given things to the club you could never imagine. He must carry on being the No.1, being the best and [being] happy.
"Maybe there's the possibility that he plays for another club, but if he feels comfortable and happy and a new board come in, he will want to stay at the club. As a friend, I will be happy if things go well for him there, but also if he has to go to another club."
Like Messi, Suarez has also been critical of Bartomeu and the Barca board. He feels he had earned the right to be treated with more respect.
"It really hurt me and my family the way they did it," he explained. "It wasn't right. That a coach [Ronald Koeman] comes in and says he doesn't count on me when the board had already said there were going to be big changes generates doubts. Koeman called me to tell me that I wasn't in his plans, but I'd known what was coming for 10 days. He just confirmed what I'd seen in the media.
"I always said the club needed a young striker, but they never brought anyone in to compete with me even. For years, they've wanted to bring more forwards because they wanted to kick me out.
"It had been coming but I at least deserved for them to phone me and explain [why they wanted me gone] before learning of it through the media."