Reid is available on a free transfer after his previous deal expired at the end of last season.
The 21-year-old spent the second half of last season on loan at Wolves, where he scored the goal that sealed promotion for the Championship title winners.
Mick McCarthy is believed to be among a host of managers monitoring the 21-year-old's situation. Birmingham, Burnley, Middlesbrough, West Brom and Newcastle are all also credited with an interest.
Reid signed professional terms with the Hammers in 2005 but has made only three first team appearances. He has had loan spells at Barnsley, Crystal Palace, Blackpool and most recently at Molineux.