The Polish outfit beat the Bhoys 6-1 on aggregate after dominating both legs of their third-qualifying-round clash, only to be disqualified for fielding an ineligible player.
Bartosz Bereszynski was brought on in the 86th minute but was meant to be serving a suspension after receiving a red card for violent conduct in last season's Europa League game against Apollon.
As a result, Uefa awarded Celtic a 3-0 second leg victory - meaning that they advanced on away goals with the tie level at 4-4, setting up a final play-off against Maribor.
But Legia co-owner Dariusz Mioduski has now written to the Scottish side in a bid to settle their fate in a one-off match.
"Meet in Warsaw or in Glasgow and let's settle this matter honourably," read a letter sent to Celtic Park on Sunday.
"The action [of our disqualification] is deeply unjust and contrary to the spirit of fair play."