France star Griezmann appeared destined to join Ernesto Valverde's side after announcing his intention to find a new club after five seasons at Atletico Madrid.
The links went cold amid reported interest from Paris Saint-Germain until Atletico CEO Miguel Angel Gil Marin reignited rumours of a done deal.
Gil Marin, in an interview with Movistar, claimed to have known about Griezmann's impending switch to Barca since March.
Bartomeu disputed that account, saying: "There's nothing to announce.
"We've always said the same. We haven't spoken to him. There's nothing to it.
"We'll see how the market changes in the next few days and weeks."
Barca has been quiet in the transfer market since the end of the season, while rival Real Madrid has invested heavily in Zinedine Zidane's squad.
The Blaugrana cruised to the LaLiga title in 2018-2019 but collapsed against Liverpool in the UEFA Champions League semi-finals, a defeat that led to speculation over head coach Valverde's future.