Arsenal's forgotten forward has been repeatedly linked with a club owned by his fellow Russian Anton Zingarevich and with Pavel Pogrebnyak already on the books.
And the 31-year-old fits boss McDermott's profile of "players with Premier League experience" he believes will give Reading a better chance of survival come May.
But asked directly about Arshavin in the wake of a goalless draw with Swansea, a non-committal McDermott said: "I don't think so. At this time of year you hear lots of rumours. I have heard that one."
The manager was more forthcoming when asked about his general plans for the transfer window, saying: "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."