The 32-year-old, who was one of six players released by QPR this summer after their relegation from the Premier League, is understood to be set for a full medical on Tuesday.
West Ham’s surprise but well-earned victory at Arsenal on Super Sunday has not led to any complacency in the transfer market from Bilic, who is keen to bring in an experienced midfielder despite the impressive display of 16-year-old Reece Oxford.
Barton had a good season for Rangers despite their disappointing time of it last season, in which they finished bottom of the top division. Barton played 28 times and scored in a 4-1 away win at West Brom.
The former Newcastle midfielder joined QPR in August 2011 following their promotion to the Premier League but was loaned to Marseille for the 2012-13 season after a several instances of poor behaviour. He was infamously sent off in Rangers’ last game of the 2011-12 season at Manchester City.
But he played an important part as QPR were promoted back to the top-flight in 2014, beating Derby in the play-off final, and he left Rangers this summer having played 99 times for the West London club, scoring seven goals.
Barton began his career at Man City before joining Newcastle in 2007.