The Primera Division champions were closely following the centre-back last year but were ultimately priced out of a move for the 19-year-old
The Camp Nou outfit were desperate to add some fresh blood to bolster their backline last year and made approaches for a number of defenders, with PSG's Thiago Silva and Chelsea's David Luiz long on their radar.
It has now emerged that Barca were also chasing Marquinhos but, after refusing to meet PSG's €35 million bid for the Brazilian, the 19-year-old opted to move to Ligue 1.
"We were closely following Marquinhos last year when he was still at Roma," Zubizarreta told TV3.
"But Paris Saint-Germain then made an offer which we could not and did not want to match."
Marquinhos has made 28 appearances in all competitions for PSG so far, but has often had to settle for a spot on the bench behind Thiago Silva and Alex.
Barcelona are once more looking to strengthen their defence this summer following the departure of Carles Puyol, but it is unclear as of yet whether they will be able to sign new players due to Fifa's transfer ban.
The Catalans have filed an appeal against world football's governing body over the sanction, but no final decision has yet been made.