Sampaoli, 57, guided Sevilla to a fourth-placed finish in La Liga in his only season in charge and the last 16 of the Champions League before losing 3-2 on aggregate to Leicester.
"All parties are satisfied by the agreement reached," said a Sevilla statement on Friday.
Argentina sacked Edgardo Bauza last month after eight matches as coach.
Sevilla's statement added: "This agreement in principle is pending the drafting and presentation of the relevant documents, which must be signed by all parties by next Thursday, 1 June."
Sampaoli revealed last week that Argentina wanted to appoint him.
"My contract with the club contains clauses which allow me to leave," said the Argentine.
"There's a clear desire from my country to have me as coach and I've had a dream of taking that chance."
Argentina and Sevilla have reached agreement for Jorge Sampaoli to take over as boss of his home country.