The 26-year-old joined Arsenal last year but has been pushed down the pecking order due to the club's summer spending spree.
The Iceland international was signed four months ago to provide cover for Bernd Leno.
Mikel Arteta is looking to strengthen his goalkeeping department in January.
The 25-year-old made 13 appearances in all competitions for Dijon last season.
The Icelandic goalkeeper has been identified by Mikel Arteta as the perfect back-up to Bernd Leno at Arsenal.