Sport says Barca have settled on a five-year contract with the Argentina international.
It's claimed Barca coach Quique Setien sees Lautaro as a partner for Luis Suarez next season rather than the Uruguayan's replacement.
With personal terms settled, Inter now must either better the offer or enter negotiations for Lautaro's sale.
The striker's deal carries a €111m buyout clause and Barca are confident of reaching an agreement over his signing - particularly with the player now ready to demand a transfer.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!