TNS have no hope of playing a Champions League play-off with Liverpool, the FA of Wales has told BBC Sport.
The Welsh champions are willing to give up their place in the Champions League first round qualifying draw if they lose to Liverpool in a one-off match.
But the FAW has insisted that TNS must enter the competition, or else their place would go to another Welsh club.
Liverpool failed to qualify for next season's Champions League after finishing fifth in the Premiership.
The Football Association has confirmed that the top four teams will be entered into next season's competition, and Uefa says it has no plans to give Liverpool special dispensation to defend their title.
But the FA says it will lobby strongly for Liverpool to be entered into the qualifying rounds.
Said FA executive director David Davies: "If they are admitted at an early stage they could play one if not two of the smallest sides in Europe and for those clubs it would be a fantastic prospect in terms of both football and finances to face the European champions."
TNS chairman Mike Harris told BBC Wales Sport a pre-qualifier against Liverpool would make far greater financial sense than for his side to play against a European minnow.
But FAW secretary general David Collins said such a proposition was not feasible and would not be supported.
TNS made their Champions League debut in 2000, losing 6-2 on aggregate to Levadia Maardu of Estonia.
Only Barry Town have managed to progress past the Champions League's first hurdle since the Welsh Premier's inception in 1992/93.
Harris, therefore, believes a high-profile match against Liverpool makes greater financial sense than playing against a European minnow.
"Such a play-off would enjoy huge media coverage," he added. "It would bring the image of our league to the whole of the UK.
"We suffer immensely compared to other nations because we're right next door to the English Premiership which takes all the media and all the cash.
"We as a nation and as [Welsh Premier] clubs are trying to put very stringent Uefa criteria in place in terms of our grounds which needs massive investment.
"Such a game would help us achieve some of our ambitions. And with a bit of luck we might beat them."