The Royals’ Russian owner Anton Zingaervich is thought to be extremely keen on the 31-year-old, who has been a bit part player under Arsene Wenger this season.
The Gunners are said to be willing to offload the man they signed for £15m this January, as he could leave for free at the end of the season once his contract expires.
Arshavin is reportedly taking the offer made by the newly promoted side seriously, as it may be his last chance of regular Premier League football.
Reading are willing to pay £2m to draft him in next month, as they attempt to add some creative flair to their struggling squad.
Manager Brian McDermott has stated that he is looking to add experience to his ranks, which would make the Russian captain an ideal candidate.
Arshavin has made over 100 appearances for Arsenal since his arrival in 2009 and has also earned 75 international caps.
Reading are likely to face competition for his signature, with former club Zenit Saint Petersburg rumoured to be interested.
Fulham are also monitoring the situation and are thought to have made an official enquiry.
It is also believed that a number of clubs in the Middle East would be willing to take on the attacking midfielder, who could be tempted by one last lucrative contract.