The 32-year-old, who was one of six players released by QPR following their relegation from the Premier League, has been training and undergoing fitness tests with the Hammers.
Bilic, who succeeded Sam Allardyce this summer, is keen to add experience to the squad which opened the season with a 2-0 victory at Arsenal on Sunday.
Former Manchester City and Newcastle midfielder Barton enjoyed a good season at Loftus Road despite QPR finishing bottom of the table. He played 28 times, scoring once in a 4-1 victory at West Bromwich.
West Ham’s pursuit of Barton may come as a surprise, however, following their co-chairman David Gold’s previous statements on Twitter about his previously poor behavior.
In 2012, after Barton was sent off on the final day of the season at Manchester City, West Ham were reported to be interested in signing him, but Gold tweeted: “We couldn’t sign J Barton even if we wanted to as he will probably be banned for a long time after his disgraceful behaviour.”
On January 14 2013, as West Ham were once again linked with the midfielder, Gold tweeted: “IMO Barton has a problem and should seek help. dg.”
And Gold posted another tweet on Barton the following day after being asked by a fan, ‘What would you do if Big Sam said he wanted to sign Barton?’, which read: “Give Sam some time off, get away for a few days. dg.”
Barton began his career at Manchester City in 2002 before moving to St James’ Park in 2007 for almost £6m. In 2011 he joined QPR and a year later was loaned out to Marseille for the 2012-13 season before returning to Loftus Road.