The former Sweden international is reportedly set to meet the Gunners boss this weekend to hold talks about a possible short-term move back to the Emirates Stadium.
The 32-year-old is currently playing for the Seattle Sounders and would join on a similar loan deal to the one David Beckham underwent when he joined AC Milan last year.
Ljungberg left the Gunners two years ago to join West Ham before heading to the America where he underwent hip surgery, leaving him injury free for the majority of his time in the States.
Wenger is believed to be interested in bringing Ljungberg back to north London as cover for Alex Song and Emmanuel Eboue, who will both be unavailable for Arsenal for up to six weeks when they head to the African Cup of Nations in January.
Chelsea were also believed to be interested in Ljungberg but the transfer embargo placed upon them has seemingly ended their pursuit of the Swede.