Celtic were unmoved after Legia Warsaw called on their "best traditions of honour and honesty" in requesting that the Scottish champions agree to a further meeting to determine which of them should progress in the Champions League.
Celtic were on Friday handed a lifeline in Europe's premier club competition after Legia were punished for fielding an ineligible player in their 6-1 aggregate win over the Scottish champions in the third qualifying round.
Friday's draw went ahead with Celtic paired against Maribor in the Champions League play-off while Legia dropped into the Europa League, but the Polish club are appealing UEFA's decision and, in the meantime, co-owner Dariusz Mioduski came up with his own solution.
After reflecting on Celtic's "beautiful" history and 1967 European Cup triumph, Mioduski said: "I therefore call on you to refer your best traditions of honour and honesty, that your famous club has been known for during the last 126 years. Do not destroy the beautiful legacy that you inherited from the past generations of 'The Bhoys'.
"I call on you to act according to the spirit of the game and rules of fair play - to issue a joint statement to the UEFA disciplinary bodies. Let's meet in Warsaw or Glasgow and settle this matter honourably."
But Celtic offered short shrift to the idea, replying in a brief statement.
"We are disappointed by Legia Warsaw's comments," the statement read. "This is entirely a matter for UEFA and its processes. Accordingly, we will reserve further comment for the appropriate time."
Bartosz Bereszynski, who came on as an 86th-minute substitute as Legia won the second leg 2-0 at Murrayfield on Wednesday night, was handed a three-match ban after a red card in the Europa League last season.
Legia believed he was free to play after missing the two games against St Patrick's Athletic as well as the first leg against Celtic in Warsaw.
However, the player was not included on Legia's squad list submitted to UEFA for the St Patrick's games and thus his suspension was not deemed to be served.
Celtic were awarded a 3-0 win, meaning they went through on away goals after a 4-4 draw.
Mioduski wrote: "We found it deeply unfair and contradictory to the fair play rules to see our dreams shattered by the last four minutes of the already decided second leg match, when Bartosz Bereszynski was brought on the pitch.
"Our player had served the full sentence and intentionally missed the first three matches in the Champions League qualifiers this season."
He continued: "Imagine Jock Stein and Billy McNeill deprived of the chance to achieve the biggest triumph in their career by an application form filled improperly by a club employee acting in good faith.
"Willie Maley, the legendary manager of Celtic FC, once said that in your stadium 'a man is judged by his football alone'. Only you can decide whether this noble credo will be replaced by an opportunistic use of legal loopholes."