Tebas told a press conference he hoped to seal a new deal by March 2018 and that the sum included feees for domestic and worldwide broadcasting rights.
The Catalan side have already lost Neymar to Paris Saint-Germain and there was talk the Argentina global could also be on his way out.
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Before the law comes into force, it will have to be approved by the Council of the Federation and signed by the president. The bill will pass to the upper house which is expected to quickly rubber-stamp it next week before it goes to Mr Putin.
In Guillem Balague's Q&A with Sky Sports on October 20, he said: "Messi is getting paid according to the new contract. Contracts are official once they are signed, not when the club announces it has been signed", he said.
"Messi has renewed his deal, at least that's what Barcelona have suggested to me".
Barcelona CEO Oscar Grau said the La Liga club would offer him a new lifetime deal but questions still linger over whether Messi has signed any necessary paperwork.
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The institutional investors in our partner's database reported: 229.70 million shares, up from 223.13 million shares in 2017Q1. Barrow Hanley Mewhinney & Strauss Ltd Limited Liability Company stated it has 5.83M shares or 0.09% of all its holdings.
Losing the talisman, who has scored 523 goals for the club in 600 matches and has a strong claim to be the best player of all time, would be a cataclysmic blow to Barcelona, and the idea of him departing for nothing would be even more unthinkable.
However, Messi claimed last week he does still harbour a desire of returning to Argentina to represent his former club Newell's Old Boys.
With regards to PSG and City Tebas was blunt: "I don't think they are cheating, I know they are".
FIFA Trial: Fox Sports Accused of Playing Role in Bribing Officials
Fox Sports has been dragged into the Fifa scandal after being accused in court of paying bribes to secure football rights. Prosecutors claim the three accepted bribes in exchange for the award of rights to soccer tournaments.