The La Liga president has told clubs they will not be allowed to spend beyond their means and warned they will have to enforce wage cuts to deal with the financial consequences of the coronavirus pandemic.
Sources close to Barca have told ESPN the club remain optimistic they will be able to structure a deal for Martinez, while the Catalan club are also interested in signing Juventus midfielder Miralem Pjanic.
"We have seen the cash flows for each club and right now they have squads which exceed the [financial] limits we will establish for next season," Tebas told the Instituto Iberoamericano de Derecho Deportivo.
"That brings consequences. Clubs are going to have to look at their academies and come up with a strategy to reduce salaries. There's no other solution. Transfers that exceed financial limits will not be allowed -- impossible."
Since 2013, La Liga has had a cap in place which forces clubs to manage their finances appropriately. Each team's limit is based on several factors, including expected income and the average amount of transfer income over the previous three years.
Barca's limit for the 2019-20 season was set at €671 million -- that includes spending on salaries for players and coaches, affiliated clubs, academies, the amortisation of transfer fees paid and agent fees. Real Madrid were capped at €641m.
That was based on Barca's expected income for this campaign -- over €1 billion -- but that has all been thrown up in the air following football's shutdown due to the coronavirus crisis.
Sources have told ESPN that Barca will knock at least €200m off their budget next season as a direct result of the pandemic, which will force them to ask the players, who have taken a 70% wage cut during Spain's state of emergency, to accept longer-term reductions to their salaries.
Tebas said last month that neither Paris Saint-Germain's "Neymar nor [Martinez] are "high on Barca's priority list" at the moment and that they "don't have the capacity to make these signings" but the Spanish champions continue to push ahead with plans to revamp their squad this summer.
The club's vice president Jordi Cardoner told ESPN they will turn to swap deals and get "creative" to land their targets, with several players offered to Inter and Juve in exchange for Martinez and Pjanic.
Tebas said the league will be watching how clubs operate in the transfer market to make sure they don't try to create the illusion of having more money than they actually do.
"There will be a lot of exchanges between the top clubs," he added. "For example, Juventus [might] sell a player to Barca and Barca sell another player to Juventus. They fix their accounts but there is no cash flow. They save on the numbers but there is no cash.
"We're keeping an eye on these operations because they don't generate money. For that reason, our controls are based on cash flow, on the money you have in the bank to be able to fulfill your obligations each month."
Barca's first hurdle is finding a way to reduce the asking prices for their targets by throwing in players -- ESPN reported that only Lionel Messi, Marc-Andre ter Stegen and Frenkie de Jong are off the table when it comes to negotiations -- and the second hurdle is to fit any new arrivals into a reduced wage structure.
Sources at the club are not hiding from the fact that challenge has been heightened by the outbreak, but there's confidence that they can maneuver things to get deals over the line while remaining within La Liga's cap.
ESPN reported on Monday that negotiations had intensified over a move for Pjanic, with Barca and Juve discussing which players could go in the other direction. Meanwhile, similar conversations are taking place with Inter as Barca look to bring down the Italian side's €111m valuation of Martinez.