The Sweden international has caught the attention of several clubs abroad, and the Serie A side have now joined the race for his services
Lazio are eager to add some fresh blood to their midfield in the winter transfer window, and they allegedly see Elm as the perfect addition to their squad.
The 23-year-old midfielder joined AZ from Kalmar in the summer of 2009 and has since developed into a key player at the Afas Stadion.
The Sweden international has already scored eight goals in 17 Eredivisie appearances this term and has played a major role in his side's successful campaign so far.
Elm, who has a contract with the 2009 Eredivisie champions until the summer of 2013, has previously been linked with clubs such as Manchester United and Valencia.