The Yellow Canaries will not consider offers below £13 million for the 27-year-old defender who has another three-years remaining on his current contract.
The Gunners are interested in Kjaer as head coach Arsene Wenger expands his search for a centre-back over the transfer window.
The North London based outfit have yet to secure the transfer of Shokdran Mustafi as talks with Valencia continue to drag on.
Wenger is running out of time to sign a new defender and will be left short of options if he fails to reinforce the defence before the end of the transfer window.
Per Mertesacker and Gabriel both out injured for Arsenal, meanwhile Laurent Koscielny is lacking match fitness and could end up missing the clash against Premier League champions Leicester City.
Wenger was forced to play Holding and Chambers against Liverpool in the first game of the season. The Gunners conceded four goals at home against the Reds in a defensive display the team will want to forget in a hurry.