Wijnaldum's Liverpool contract expires at the end of the month and his next move to PSG has been confirmed.
But the Netherlands captain, who led his team with eight goals in Euro 2020 qualifying, was expected to link up with former Oranje coach Ronald Koeman at Barca.
Following weeks of speculation, though, there was no deal, allowing PSG to make their move.
Wijnaldum said on Saturday: "I negotiated with Barcelona for four weeks and unfortunately we didn't [agree].
"Paris Saint-Germain were faster and more decisive. And the project they have there appeals to me very much.
"It was a tough choice. I have to say that I too thought I would go to Barcelona, also because Barcelona was the only club that was really interested at the time.
"But we couldn't [agree] and with PSG we did."