Messi, who is widely considered one of the greatest players of all time, has endured a tumultuous campaign at Barca, his only senior club.
The Blaugrana failed to defend their LaLiga title, losing the crown to rival Real Madrid, while Messi clashed with the board as coach Ernesto Valverde was sacked.
So news of Messi's father buying a house in Milan prompted optimism among Inter fans they could be set for an incredible coup.
However, Nerazzurri chief executive Marotta insists this is not the case.
"We are talking about fantasy football," Marotta said. "[Signing Messi] is absolutely not our goal.
"There is no negotiation and I think he is focused on continuing with Barcelona."
Inter beat Genoa 3-0 on Sunday (AEST) to climb to second in Serie A, although rival Juventus can clinch the Scudetto with a win against Sampdoria on Monday (AEST).
After the match, coach Antonio Conte was also asked of the possibility of signing Messi but simply repeated Marotta's message.
"I think Marotta has already said: it is fantasy football," Conte said. "At this moment, there are many reasons Messi cannot join Inter."