make out that

make out that (something is the case)

To act or speak in a manner that purports a falsehood or deception. At the tail end of the presentation, Sarah started making out that it was my team that caused the huge delay. After the disruption, everyone in class made out that nothing had happened.
See also: make, out, that
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.

make out that...

to pretend that [something is so]. He made out that he hadn't seen me. We all made out that we hadn't heard the sound.
See also: make, out, that
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.
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References in classic literature ?
I could just make out that he had a book as well as a knife in his hand, and was still wondering how anything so incongruous had come in their possession when the kneeling figure rose once more to his feet and the whole party began to move together towards the house.