Torreira quickly fell down the pecking order at the Emirates under Mikel Arteta and also failed to convince Diego Simeone during a loan spell at Atletico Madrid in 2020-21.
However, the Uruguay international was a standout performer for Fiorentina in the 2021-22 season, racking up five goals and two assists from 31 Serie A appearances.
Torreira helped Fiorentina qualify for the Europa Conference League, but La Viola ultimately opted against triggering his £12.5m buy option in his loan deal.
The former Sampdoria man is now back at Arsenal's London Colney training base and will be part of the Gunners' squad for their pre-season tour of the United States.
Torreira has been expected to find a new club after a move to Fiorentina fell through, and his agent Pablo Bentancur has now confirmed that Valencia are in pole position to sign his client.
"We have reached an agreement with Valencia, [Gennaro] Gattuso wants him," Bentancur told 100% Deporte, as quoted by transfer expert Fabrizio Romano.
"We are gonna discuss with Arsenal. Arteta wants to see him in the pre-season. He had great numbers with AFC but we have a pre-agreement with Valencia."
Torreira - who now has less than 12 months to run on his Arsenal contract - has also insisted that there is "no chance" of him remaining at the Emirates beyond the summer.
"There is no chance. From the beginning, they told me that I didn't have a place, so I don't want to stay either," Torreira told El Telegrafo. "We'll look for a new direction. Any team that wants me has to buy me, which would be around €15m (£12.9m)."
Torreira is seemingly set to leave Arsenal after making 89 appearances in red and white since 2018, racking up four goals and six assists in the process after being signed by Unai Emery.
Valencia are set to beat Lazio and Roma to the signature of the Uruguay international, who had previously admitted that a move to the Europa Conference League champions was a possibility.
The midfielder has won the FA Cup and Community Shield during his time at the Emirates and also ended his unfavourable stint at Atletico with a La Liga winners' medal.
Arsenal could ramp up their efforts to sign Sergej Milinkovic-Savic or Youri Tielemans, with the latter allegedly putting his house up for sale amid speculation surrounding a £30m switch from Leicester City.
However, the Gunners are said to have seen a £42m offer for Milinkovic-Savic turned down by Lazio, who were offered the chance to sign Torreira before Valencia swooped.