Cancelo, 29, still has three years left on his Manchester City contract but has not been at the Etihad for 14 months after a fall-out with Pep Guardiola.
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He moved to the Nou Camp in September but, despite being a regular and Barcelona having first option to sign him, they insist the £40million asking price is too steep.
That has alerted Gunners boss Mikel Arteta, who knows Cancelo well from his time as Guardiola’s assistant.
His ability to play on either flank is a huge plus for Arteta, who is in the market for a top level left-back, while Cancelo also impressed in midfield when he was pushed forward at City.
Cancelo has made it no secret that he would prefer to stay at Barca.
Yet they do not want to go beyond paying another loan fee to keep him for a further 12 months.
He spent the previous six months at Bayern Munich but the German giants also insisted the asking price was too high.
City want the Portugal international off the books, rather than seeing his price drop the longer he remains their player.
Arteta has raided City for Oleksandr Zinchenko and Gabriel Jesus in the past.
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And, as much as he would like to stay at Barca, Cancelo may be tempted by another link-up with the Spaniard in the summer.
He made 154 appearances for Man City, scoring nine goals and providing 22 assists.
The full-back won three Premier League titles and the Carabao Cup at the Etihad, before he left for Barcelona and won the LaLiga title last year.
This season he has played 32 games in all competitions, starting 22 of their 29 league matches.