"It's time for him (Arshavin) to look for new challenges, and this is a great opportunity for him," he told Spanish television station La Sexta.
"Everything depends on how interested Barcelona are and how much the player wants to play there.
"There are not that many clubs in the world that can match his pay at the moment, but the main reasons for leaving will be sporting ones."
Barcelona say they have been monitoring Arshavin since earlier this year.
"Our interest isn't sudden since we have been following him with discretion for a few months now," said Soriano, who added that the Spanish giants had first noticed him in April when he played against German side Bayer Leverkusen in the Uefa Cup.
"We were under the impression that he played in midfield, but now we have seen that in big games, with his national team at the Euro, that he plays on the flank," Soriano told Mundo Deportivo.
"That's dispelled any doubt and this is the profile of a player we would like."
On Wednesday, Arshavin said: "Barcelona are my dream, I never thought I would have a genuine chance to play for the club.
"I have supported Barcelona all my life, let's see how the situation unfolds. For now I can't say anything for sure."
Arshavin had previously told BBC Radio 5 Live of his admiration for England's top level.
"I see English games on TV - it's the best league in the world," he said.
"I would like to change club. It's not a big difference between England and Spain. It's another level for me."
Zenit coach Dick Advocaat is already resigned to losing his star player.
"I can understand that he wants to play in Europe," Advocaat told BBC Radio 5 Live.
"I think he has some clubs in his mind, some in England and others in Spain, because they are the only two countries he would like to play in.
"If you lose one of your main players you don't like it as a coach but you have to be realistic."
Arshavin was suspended for Russia's opening two games at Euro 2008, but his return has propelled Guus Hiddink's side to a semi-final meeting with Spain, the team that beat them 4-1 in their first group game.
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