The Italian title hopefuls admit they would welcome the addition of such a quality player to their ranks, but feel there is little chance of them being able to do so.
As a result, they have moved to play down speculation suggesting an approach is imminent.
Arshavin is no longer considered to be a key figure at Arsenal, having struggled for consistency, but the Gunners would be reluctant to part with an experienced performer mid-season.
Lazio accept as much and insist they have made no attempt to open negotiations for the Russia international.
"Arshavin is a great player and I think everyone would like to have him in their squad," sporting director Igil Tare told calcionews24.com.
"But I don't think there is any chance of seeing him in a Lazio shirt.
"There are a number of reasons why it would be difficult. First of all, we have never spoken with Arsenal and secondly, perhaps more importantly, I don't think the Gunners would want to part with a top player."