Per the source, the Gunners are interested in the young defender who impressed on loan at Galatasaray last season.
The North London based outfit are currently facing a defensive crisis with only Calum Chambers (21) and new signing Rob Holding available for their Premier League opener against Liverpool on the weekend.
The Manchester Evening News report that Denayer is considering his option after falling further down the pecking order.
Denayer wants first team football last season after playing regularly for Galatasaray over the 2015-16 campaign playing an important role in lifting the Turkish Cup.
The Gunners could however, face competition from Galatasaray after their sporting director confirmed interest in the Belgium international.
Sporting director Levent Nazifoglu told Turkish-football.com: “Denayer settled in well last season and we want him back but it all now depends on what he says and what Manchester City decide.
“We want him and so does the manager and City know this.”
Denayer established himself as a star player at Galatasaray last season and current head coach Jan Olde Riekerink has an impressive track record working with young players.
The Belgium intentional provided three assists in 28 appearances for Galatasaray in all competitions last season and settled into life in Istanbul.