The two clubs have been in marathon negotiations over the Argentina international, whose deal carries a €111m buyout clause.
In Italy, it's claimed the option will expire on July 7, which would then allow Inter to price the striker out of a move away.
However, Sport says inside Barca, there's a confidence the clause doesn't run out until July 15 - so giving them an extra week to find a deal. Either way, Barca know time is running out on closing an agreement for Lautaro.
Inter are demanding either Barca meet the player's clause in it's entirety, or make a cash-plus-players offer the equivalent of the €111m option.