The 32-year-old is currently without a club after being released by the West Londoners in June following their relegation from the Premier League.
It is being reported that the former Newcastle United and Manchester City midfielder is expected to have a medical in east London within the next 24 hours.
News of the move has been met with a mostly negative response by the club's fans.
Many supporters have voiced concerns that Barton's bad boy tendencies will rear their ugly head again and disrupt the club's good team spirit, particularly in the wake of West Ham's superb winning start to the season at Arsenal.
But more pertinently, some have also questioned whether Barton would even get in the West Ham team given the players Bilic already has at his disposal in that position - namely Cheikou Kouyate, Mark Noble, Pedro Obiang, Diego Poyet, Reece Oxford and, to a lesser extent, Kevin Nolan.
Why the happy Hammers are willing to take a risk on Barton
So why are the Hammers keen to bring Barton in?
For starters, regardless of past misdemeanours, Barton is a good solid Premier League performer and has kept his nose relatively clean for the last couple of seasons.
He would definitely add to West Ham's squad depth and is a winner on the field.
But there could be three key reasons for the move.
Going for a Song, going for Barton
The first is that Bilic's summer-long pursuit of Barcelona's Alex Song has had to be put on hold due to a lengthy injury which could sideline him until the new year.
Co-owner David Gold recently admitted the club was still hopeful of signing Song, as reported by the Independent.
But it may be now that they will need to revisit that in January and Barton is the man the Hammers are turning to in order to plug the gap.
The French connection
The surprise move for Barton may also have been influenced by the fact the Liverpudlian could offer vital protection for Hammers' star signing Dimitri Payet.
In fact Barton and Payet just missed out on playing together at Marseille as the French international was signed after Barton returned to England following his season-long loan spell with the club.
Bilic may see Barton as something of an enforcer in the same midfield as skilful attacker Payet, who was one of the best players on the pitch against Arsenal.
Let's not forget in all of this that Barton would be arriving on a free transfer.
That would prove attractive to a lot of clubs but particularly the Hammers who, having spent around £25million this summer - although the net spend is less than £20m - are said to be running out of money to spend of players.
Barton's chequered past will always make life difficult for any clubs looking to bring him in, but he is very much one of those players who fans tend to love when he is on your side.