Make goo-goo eyes at (someone) American humorous informal
To look at (someone) in a passionate, infatuated and romantic way
Jennie can't hide her love for Peter because she keeps making goo-goo eyes at him.
The way those two make goo-goo eyes at each other is making me become jealous.
The verb "make" should be conjugated according to its tense.
The origin of this phrase is supposed by some to have related to "agog" and "goggle". Its first record was found in Random House Historical Dictionary of American Slang, Volume 1, A-G by J.E. Lighter, Random House, New York, 1994.