The Gunners want to include Torreira in a move for Atletico midfielder Thomas Partey but the La Liga club have so far dismissed any talk of a swap or player-plus-cash agreement.
Talks are at an advanced stage over Torreira joining on an initial season-long loan but the clubs are yet to decide on whether the transfer will include an option or an obligation to buy.
Arsenal would ideally like to recoup the majority of the £27 million they paid Sampdoria for Torreira in July 2018 and remain hopeful they can convince Atletico to link that valuation to a deal for Partey.
Partey has a £45m release clause in his contract and Atletico have been determined to stick to that valuation.
Arsenal have made Partey one of their top two midfield targets -- alongside Lyon's Houssem Aouar -- but need to raise funds for further signings through player sales and had hoped Torreira could form part of an agreement which Atletico would accept.
Torreira has been frozen out under Arsenal head coach Mikel Arteta, who refused to be drawn on the situation at a press conference to preview Monday's Premier League trip to champions Liverpool.
James Olley, Rodrigo Faez and David Cartlidge contributed to this report.