Griezmann was thought to be bound for Camp Nou after announcing his decision to leave Atletico Madrid, but Barcelona president Josep Maria Bartomeu claimed the Blaugrana have not spoken to the 28-year-old.
When asked about the prospect of lining up alongside Griezmann in 2019-20, Suarez referred back to comments he made in December 2017 when he described the World Cup-winning forward as "an elite player", but stopped short of reiterating his support for a move.
Suarez told RAC1: "What I have to say, as I said last year, is that he is a quality player.
"But he is an Atletico player and I prefer not to comment on it."
With reports linking Brazil talisman Neymar with a move back to Barcelona following a tumultuous second season at Paris Saint-Germain, Suarez indicated he would welcome him back with open arms, saying: "Who would not want to enjoy players like Ney?"
Suarez will turn 33 in January and he said he accepts the club will be looking for goal-scorers who can pick up the mantle as his career enters its twilight years.
"A Barca player has to be prepared for competition and the club bringing in a partner who can impersonate you in some moments. We all want to help the club," he added.
"I do not say who to bring in or who not to bring in.
"I took over last season and I assume that over the next few years the club has to bring a young player, a number nine, not only to compete with me but for the future of the club, because I also want what's good for the future of the club.
"I assume my responsibility because I am 32 years old and I am going to be 33."