The Netherlands international, 27, joined Manchester City from AC Milan last summer for £46.5 million and made a strong start to life in the Premier League, scoring and assisting on his debut in a 4-0 win over Wolverhampton Wanderers. His influence has diminished significantly since the turn of the year, however, as Pep Guardiola settled on a preferred midfield axis that has left Reijnders as a rotation option.
The Sun reports City would consider offers in the region of £45 million. Reijnders and the club are expected to meet at the end of the season to discuss his future, with no public push from the player's camp for a departure at this stage.
Arsenal are not alone in their interest. Juventus are understood to be pursuing him, and multiple Serie A clubs have been credited with interest in a return to Italian football. Newcastle United, Aston Villa and Reijnders' former club AC Milan are also monitoring developments.
At Arsenal, the Dutchman would compete for a midfield place alongside Declan Rice, Martin Zubimendi and Martin Odegaard. His ability to operate across multiple central roles would suit Mikel Arteta's rotational demands in a season that stretches across the Premier League, the FA Cup and the Champions League.
Arsenal have just clinched the Premier League title, their first since 2004, and will face Paris Saint-Germain in the Champions League final later this month.
Whether City actively seek to sell so soon after acquiring Reijnders remains unclear, particularly with the managerial position at the Etihad yet to be resolved.