The 31-year-old has been heavily linked with a move to the Madejski Stadium, with a growing contingent of Russian's affiliated with the Berkshire-based club.
Royals owner Anton Zingarevich hails from the same country as the former Zenit St Petersburg star, while Arshavin's international team-mate Pavel Pogrebnyak also currently plies his trade with the Premier League strugglers.
Arshavin has endured a difficult year in north London on the periphery of Arsene Wenger's first-team squad. And, having been heavily linked with a move away from the Emirates Stadium in the summer, the Gunners boss has been forced to reiterate that the player remains part of his plans moving forward.
But, that has done little to stem speculation linking the player with a January move, with Reading reportedly at the head of the queue of interested clubs.
Asked directly whether he held an interest in the Arsenal star in the wake of yesterday's goalless draw with Swansea, McDermott responded: "I don't think so. At this time of year you hear lots of rumours. I have heard that one."
However, the Royals boss was more forthcoming with general information regarding his plans for the forthcoming transfer window, emphasising the fact that he expected to strengthen his squad in the New Year.
"We are talking at the moment regarding players. If we could bring in two or three players that could make a difference, it would be useful to the squad.
"We don't generally deal in big prices. We try to get players that are available. I'd like to bring in two or three with a little bit of experience at the level."