The 27-year-old Netherlands announced in an interview that he would be leaving for Catalunya on Thursday after seeing his club eliminated in the play-off
Speaking in the aftermath of a humbling 4-1 loss to Russia's Champions League debutants, which meant a 5-2 aggregate defeat, the 27-year-old confirmed he is in line to take Claudio Bravo's place in Luis Enrique's squad.
Bravo travelled on Tuesday to finalise a move to Manchester City but Cillessen insists the pieces of this transfer puzzle falling into place did not affect his performance on a chastening night for the four-time European Champions.
"I will take the plane to Barcelona tonight or tomorrow," he told Dutch broadcaster Veronica. "There we will look for the latest details.
"An agreement would be nice. But this is an awful exit for me.
"I wanted to play today. The transfer saga played no role in my sharpness."
Ajax laboured past PAOK in the previous round and, having shared a 1-1 draw with Rostov in Amsterdam last week, they were blown away by the surprise package from last season's Russian Premier League.
Sardar Azmoun nodded in Aleksandr Erokhin's 34th-minute cross to break the deadlock and it was a case of provider-turned-goalscorer seven minutes after half-time when Erokhin got the better of Ajax aerially.
Christian Noboa and Dmitry Poloz rounded off a blistering spell of three goals in 14 minutes, meaning Davy Klaassen's late penalty after Fedor Kudryashov was dismissed for bringing down substitute Kasper Dolberg came as scant consolation to Ajax and their boss Peter Bosz.
"We were well prepared before this game and were looking forward to it," Cillessen added. "But when you start like this, it will automatically cause problems."