You have to save it in txt first from the menu of Documet Info panel, then print it from txt file. But the report will include only colors that have been used in your document.
Another option is File=Package option to package your file. You will get something like this.
Package Report
-----------------------------------------------------------------------------
Document:
Name: Alina Sahakyan.ai
Color Mode: CMYK color
Color Profile: none
Ruler Units: centimeters
Artboard Dimensions: 21 cm x 29.7 cm
Show Images in Outline Mode: OFF
Highlight Substituted Fonts: OFF
Highlight Substituted Glyphs: OFF
Preserve Text Editability
Simulate Colored Paper: OFF
-----------------------------------------------------------------------------
Spot Color Objects:
C=18 M=19 Y=33 K=0 1 (RGB)
C=9 M=15 Y=39 K=1 (CMYK)
R=101 G=89 B=82 (CMYK)
R=142 G=26 B=53 (CMYK)
R=209 G=113 B=112 (CMYK)
-----------------------------------------------------------------------------
Missing Fonts:NONE
-----------------------------------------------------------------------------
Protected Fonts that were not packaged:NONE
-----------------------------------------------------------------------------
Fonts:
Myriad Pro (OTF)
ArTarumianBarak Bold (TrueType)
-----------------------------------------------------------------------------
Embedded Fonts:
NONE
-----------------------------------------------------------------------------
Missing Links:
NONE
-----------------------------------------------------------------------------
Linked Images:
NONE