The Italy global even expressed a desire to join the Nou Camp club, only for him to return to Paris Saint-Germain for pre-season training.
Verratti, who Andrea Pirlo recently named as his successor, has four years left on his current PSG contract having signed an extension last August.
Verratti says he is happy to stay at PSG but remains open to a switch if the two clubs can agree a fee.
Yesterday technical director Robert Fernandez confirmed Barca are still in pursuit.
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Valverde also stressed he is in no great hurry for new signings, as Barca already boast a squad of players that is hard to improve.
'If you want to make something happen with a player who has an ongoing contract then you first need to come to an agreement with his club'.
New Barcelona manager Ernesto Valverde is hoping to recruit more players as he looks to bolster his side ahead of next season. "I'll work with both Gomes and Rakitic". But the coach has stated he is interested in securing the 14-year old, but not willing to let his players go. Valverde supposedly thinks the midfielder can bring excitement back to Catalonia after their inconsistent season under Luis Enrique last time out.
"They are my players and I consider them in my plans", he told a news conference when asked about Rakitic and Gomes.