The Gunners chased the Portugal international over the summer, yet negotiations for a deal worth around £30m with Sporting Lisbon broke down.
However, with the Londoners through to the latter stages of the Champions League and the Estadio Jose Alvalade side known to be strapped for cash, Arsene Wenger is keen to push through a January swoop.
The Frenchman has made a top class holding midfielder a top target for next month, with injuries to the likes of Aaron Ramsey, Mikel Arteta and Jack Wilshere having revealed a lack of depth at the Emirates Stadium.
Carvalho is seen as one of very few targets of the required level available, and Wenger is hopeful that his rumoured winter budget of £20m will be enough.
The 22-year-old is already a regular in the Portugal international set-up and has been known to fill in as an emergency centre-back in the past.