Messi, 34, is a free agent after his contract with Barca expired on June 30. The Catalan club are hopeful of signing him to a new deal but first must make cutbacks to reregister him for next season due to La Liga's Financial Fair Play rules.
The Argentina international's last contract was worth more than €500 million over four years, including signing-on fees, bonuses and his weekly salary. Tebas says Messi must take a hit to remain at Camp Nou.
"Exactly," he said in a call with the UK media when asked if Messi would have to take a big pay cut this summer. "He won't be able to sign on the previous conditions, that's impossible. But I don't think any European club would be able to pay that amount."
However, Tebas had a warning for the two State-owned clubs, who have both shown an interest in Messi.
"City have lost €270m [during the pandemic] so obviously they wouldn't even consider signing Messi [on his previous salary]," the La Liga chief added. "PSG have had losses, too, so they can't even consider signing Messi [for that much].
"If they do, it will be financial doping. It would be incredible if it happened. We need to establish limits. Financial doping is damaging football.
"It's not real money because it's not generated by the clubs. Money not from football causes bad inflation and ruins football because clubs must put in all this effort [to compete], which takes them above their financial capacity.
"We have to fight against this. This is one of the pending issues in European football. If it's not solved, the game will find itself in a very complicated situation."
Tebas insisted that the league would not be flexible when it comes to registering Messi's new deal, saying that he believes Barca will make the necessary cutbacks and that the attacker is "closer" to re-signing for the Blaugrana than going elsewhere.
However, having earlier said he "doesn't know" if Messi will be registered in time for the start of La Liga on Aug. 14, he also insisted the league should not obsess over individual players.
"We always want the best players, but Neymar left, Cristiano Ronaldo left and we're still here, still growing," he said. "And as far as I know neither Serie A nor Ligue 1 have grown as much as they would have liked.
"When the Italian [league] took Ronaldo, they said to me broadcast rights would go up. They have just lost €200m on international television rights and on a national level it's 10% down. I would be sorry if Messi left, he's the best ever, but we should not become obsessed with [individual] players."
Barca's salary cap before the pandemic was over €600m, while it dropped to €347m this year. It will fall again next season, but Tebas says they will bounce back.
"Barcelona are facing uncertain times but they will be able to solve their problems because they have the highest turnover in the world," he added. "When they get back to normal turnover, they will have restructured their debt and reduced their wage bill.
"Like others, due to pandemic, they have gone over their spending limit. When clubs go over, we have a rule called one by four. We allow new players [to be registered] whenever they reduce the current wage bill.
"For each euro they want to use for signups, they have to save €4. For example, if the players that Barca have signed, [Sergio] Aguero and others, are going to cost €50m for the next season, it means €200m must be saved, either by transfers or by reducing the wage bill."