The centre-back from New Zealand is out of a contract in the summer, with Arsene Wenger and Brenden Rodgers monitoring closely.
It was also reported that Manchester United were interested but it seems these claims have faded.
The Gunners have had defensive troubles this season, with only 2 senior centre-backs in the squad, leaving Calum Chambers and Nacho Monreal to fill in when needed.
Meanwhile Liverpool’s £20m summer signing, Dejan Lovren, has failed to impress thus far, meaning Brenden Rodgers has had to turn to Kolo Toure in recent weeks.
Winston Reid would be an attractive signing for both clubs, either on a free in the summer or very cheap this January.
West Ham have reportedly tried to tie the 26 year-old down to the club with a new long term deal but according to reports made in The Mirror, Reid will exit the club next month.
By Phil Wellbrook