Messi asked to leave Barca in the summer, only to end up staying to avoid a legal battle with the Catalan club.
However, he will be out of contract in 2021 and able to walk away on a free transfer if he does not agree a new deal.
Suarez did leave Barcelona to join Atletico Madrid last month after being told he was not part of the club’s plans, which upset Messi and saw the Argentine hit out at the club’s board.
But the Uruguayan told ESPN: “Messi wanting to leave Barcelona was not a gesture towards me. They should have respected his decision to want to leave.
“Out of respect for the relationship I have with Leo, I am not going to talk about what we said at the time, but it was a difficult and complicated situation.
“He wanted to leave and the club didn’t want him to. I tried to support him, to take care of him and to distract him a little. The cameras were on him. It was tough, but I had to help him.”
Asked if he thought Messi would leave the Blaugrana at the end of the 2020-21 season, Suarez said: “Leo is aware of what he represents for Barcelona. He has given things that the club never imagined.
“He has to carry on being the number one, the best, and being happy. There could be a possibility that Messi goes to another club, but if he is comfortable and happy again and another board comes in, he will want to stay at the club.
“As a friend, I will happy if things are going well for him there and if he has to go to another club, also.”
Barcelona president Josep Maria Bartomeu brought next summer’s elections forward to next March after the club’s 8-2 loss to Bayern Munich in the Champions League in August and will be leaving anyway as his mandate comes to an end.
The 57-year-old is also set to face a vote of no confidence later this month after more than 19,000 Barca members signed a censure motion against the club chief and his board.