Team-mate Andres Iniesta recently signed a "lifetime" deal with the club and Barca CEO Oscar Grau recently suggested he'd like to see Messi do the same.
Tebas says Barcelona have informed him a contract has been signed unless he has been "lied to".
He explained: "Messi has a contract and it has been renewed".
A summer of turmoil in which the Catalans saw Real Madrid win La Liga and the Champions League before losing Neymar to Paris Saint-Germain was topped off with the new Messi has signed a new deal being retracted.
And La Liga president Javier Tebas has claimed the reports are accurate, despite the club having yet to confirm it.
Tebas told a press conference he hoped to seal a new deal by March 2018 and that the sum included feees for domestic and global broadcasting rights.
"And Messi has signed with Barcelona.
Contracts are official once they are signed, not when the club announces it has been signed", he said. "All that is missing is the picture with the president".
However, Messi claimed last week he does still harbour a desire of returning to Argentina to represent his former club Newell's Old Boys.
"The desire is always playing for Newell's, it is what I dreamed as a kid", Messi told Argentine channel TyC Sports.
"I can not say I'm going back because I do not know where I'm going to be".