The Hornets re among the clubs showing keen interest in signing the 25-year-old right back from Olympiacos.
The 25-year-old is a Norway international but counts as a homegrown player in the Premier League thanks to the time he spent at Manchester City after joining as a 16-year-old.
Elabdellaoui is out of contract at the end of the season and so is free to talk to foreign clubs in January with Premier League club Huddersfield showing interest, as well as Benfica, Sporting Lisbon, Spartak Moscow and Stuttgart.
Watford boss worked with Elabdellaoui last season during his loan spell at Hull and is keen to work with him again while he would boost their homegrown quota.