Arshavin has made just one Premier League appearance for Arsenal this season since returning from a season-long loan to Zenit St. Petersburg last term.
The 31-year-old, who set Arsenal back around £15 million when he signed from Zenit, has failed to live up to expectations since his move to the Emirates Stadium in 2009.
Arsenal manager Arsene Wenger's previously insisted he would like the 31-year-old to remain in north London, although he admitted it would be hard to give him opportunities given the competition ahead of him in the Arsenal squad.
Now, according to the Daily Star, Fulham hope to exploit that and the fact that Arshavin is only contracted with the Gunners until next year by trying to sign the winger in January for around £1 million.
The paper reports that Fulham hope to play on the fact that the Russian is settled in London in order to persuade him to move across the capital.
Fulham boss Martin Jol lost both Clint Dempsey and Mousa Dembele to Tottenham over the summer and is keen on recruiting more firepower up front. The Dutchman has also confirmed he has money to spend in January.
“The club’s chairman Mohamed Al Fayed said before the season you can spend the same amount as last year," he said.
“But we sold for over £30m and only bought for £8m. So I am 100 per cent certain he knows there is a lot in the kitty.”