Here is a Macro that I use to do just that.
When run it will prompt the user to "Hit R to refresh the list"
Doing this will run the portion of the macro that exports a list of layer names to a file (LayNames.TXT). Hitting any other key will cause NOTEPAD to open the existing "LayNames.Txt" file. On a large drawing I often keep Notepad open on the desktop with a Layer list going.
If you don't wish to open an instance of Notepad then simply delete that portion of the macro.
Obviously you can copy & Paste from notepad to Excel, or open the LAyNames.txt file directly from excel.
Actually you should be able to replace the 
CMDSTR$ = "NOTEPAD.EXE "+" LayNames.TXT"
with a call to Excel, but I have not tried that....

Let me know if you want the behavior of this altered in some way, or if you have operational difficulties of any kind.

Note: you must "Hit R" the first time you run this or Notepad will open an empty file.
There is no error checking for LayNames.txt not found.



'---------------start of macro--------------
'listlayr.d3m
Window 3,40
print "Hit R to refresh the list"
print "any other key to load existing"
anykey k
wclose
Maxlayer = 100


if k = 82 then 
orglayr = sys(3) 'storage for original layer number
open "o", 1, "LayNames.TXT"
print #1,SYS$(2) 'print filename
precision 0
for Curlay = 1 to Maxlayer
layer(curlay) = 14
print #1, curlay, "-",Sys$(93)
next
close
Layer(orglayer) = 14 
end if

'open the file in Notepad
CMDSTR$ = "NOTEPAD.EXE "+" LayNames.TXT"
RUN CMDSTR$,1
'----------------------------------------------------