The Guadalajara winger told Medio Tiempo in his homeland that former club Deportivo Toluca had rebuffed interest from the champions in 2014.
But the 29-year-old has admitted, five years later, that he would jump at the chance to join the Hoops if they came back in for him now.
Brizuela, who ended up moving to Guadalajara in a £5 million move, said: “I heard the rumours, but I didn’t want to think about them too much and distract myself.
“In the end, I don’t know if [Celtic] spoke to a [Toluca] director, but when I was in Toluca they approached me.
“The club didn’t let me go because Celtic didn’t want to pay their asking price. I won’t give up hope that such a moment will come, despite my age."
Brizuela is unlikely to get his dream move, with Celtic currently well-stocked on the winger front. Scott Sinclair, Lewis Morgan, Jonny Hayes, James Forrest and Mikey Johnston are all capable of operating on the flank while Marian Shved is also on the fringes of the first team.