Why are they willing to let him leave?
Runarsson was bought to operate as Bernd Leno’s understudy after the club sold Emiliano Martinez to Aston Villa last summer.
Arsenal have, however, recognised the need for the Icelandic international to gain first-team experience and are open to letting the 25-year-old move on loan if they can secure a replacement as back-up to Leno.
A number of clubs in the Championship and across Europe are interested in taking Runarsson for the second half of the campaign.
How has he performed for Arsenal?
He kept a clean sheet on his debut against Dundalk in the Europa League, which Arsenal comfortably won 3-0.
In his only appearance outside the Europa League this season, Runarsson endured a disappointing performance in the 4-1 League Cup defeat at home to Manchester City last month.
Who do they want as their number two?
While Arsenal will again explore signing a permanent number two, if that is not possible in January then a seasoned player may be loaned before the matter is readdressed in the summer.
It is unclear if Brentford goalkeeper David Raya, whose club are pushing for promotion to the Premier League, remains the first-choice target.
Arsenal also have a highly-rated Estonian goalkeeper Karl Hein and the 18-year-old qualifies as homegrown in the summer. That helps mitigate for the exit of Matt Macey to Hibernian.
Is there anything else I need to know?
For more transfer nuggets and exclusive details, including a contract renewal for an Arsenal first-team player, Go Deeper with David Ornstein’s column.