Messi told Barca he wanted to leave in the summer, with sources telling ESPN he had already held talks with City, but the Catalan club refused to let him leave.
The Argentina international is out of contract in June, though, and will be able to walk away from Barca -- and potentially La Liga -- for free if he doesn't extend his terms.
"The only club in the Premier League that talks about registering Messi is Manchester City," Tebas said in a news conference on Tuesday when asked if he was worried about the prospect Messi departing La Liga for England.
"Since Man City compete outside the rules, what I am worried about is that they are able to access a player by breaching UEFA's [FFP] rules. It is not only me complaining about this. [Liverpool coach Jurgen] Klopp and [Tottenham's Jose] Mourinho have also complained about City."
City's finances have been the cause of scrutiny since Sheikh Mansour took over the club in 2008. Earlier this year, the Court of Arbitration for Sport [CAS] overturned a two-year ban from UEFA-club competitions for financial irregularities.
The CAS said that most of the alleged breaches were not established or time-bound.
"I have criticised what City do so many times, doing it one more time makes no difference," Tebas added. "They are not affected by COVID-19, by pandemics or by anything because they are financed differently and it's impossible to fight against that."
Tebas was speaking after announcing the new salary limits for the 42 teams that make up Spain's top two divisions, with the 20 clubs in La Liga forced to chop over €600m off their spending costs for the season.
Barcelona have been hardest hit by the COVID-19 pandemic, with their salary cap dropping almost €300m in respect to last season, down from €671m to €382.7m.
The cuts could complicate negotiations with Messi over a new deal. Barca won't elect a new president until Jan. 24, which is when those talks can begin, but Messi will be free from the start of January to negotiate a pre-contract agreement with any club.
As Barcelona, Real Madrid and most of Spain's top clubs are forced to reduce salaries and sell players to balance their books, Tebas stated his surprise that spending continued as normal in the Premier League over the summer despite the COVID-19 pandemic.
"I am not saying the Premier League is irresponsible because I am not really involved with their figures, but I am surprised about the volume of transfers, even with the corrective factor of Chelsea not signing players for two years," the La Liga chief said.
"I am sure they are responsible but what we are trying [in Spain with the reduced salary limits and player sales] is to make sure our game is sustainable -- not just this season, but for coming seasons.
"We will see how this evolves for the Premier League. There are important figures that need to be considered: the fact they have maintained the level of new players being signed and the issue with China [television rights] -- dropping from €200m to €10m is a significant reduction in revenue.
"When you add COVID-19 to that, you need to pay attention to ensure that the Premier League remains stable. What we want is for all leagues to remain financially stable."