Barca president Joan Laporta confirmed in August the club could have kept Messi if they had agreed to LaLiga's deal to sell 10% of its business to CVC Capital Partners.
That operation would have been worth around €270 million to Barca, but they refused to sign off the sale, with Laporta saying it would have mortgaged off the club's future.
Tebas says the deal would have allowed Barca to renew Messi's contract at Camp Nou, adding that it would also have been possible to keep the Argentina international if they hadn't brought in Memphis and Aguero earlier in the summer.
"I didn't know if Messi could renew because of that, but later I got a call [from Laporta]. 'Can we accelerate the CVC deal? The kid [Messi] is getting nervous,' he said.
"I told him: 'The day it comes out, Florentino is going to try and burst it.' And Laporta told me: 'No, no, I have character.' Florentino's behind it all, I have no doubt.
"There was an agreement that if [Barca] signed the CVC deal, they could have put 15% of the money towards signing players. In my opinion, they could have signed Messi.
"Laporta signed players like Memphis, Aguero... if he didn't sign those players, Messi could continue."
Barca, along with Madrid and Athletic Bilbao, opted against signing the deal with CVC. The other 17 top flight clubs in Spain all accepted the operation, which rewarded them with an immediate cash injection.
CVC, in return, will take a 10% cut of LaLiga's business, including television rights, for the next 50 years, although they won't take a percentage of Barca, Madrid and Athletic's earnings.
As a result of not signing up to the deal, and after registering losses of €481m last season, Barca's LaLiga spending limit for the campaign has been cut to just €97m.
Last season, that limit was set at over €300m, while in 2019-20, prior to the pandemic, it was over €600m. The limit covers spending on first-team wages, academy costs and amortisation payments on transfers, among other things.