Newcastle United, Sheffield Wednesday, Norwich City and Swansea City have also been linked with the Chelsea forward.
It has been reported by the British newspaper that QPR are interested in securing the services of the striker on loan for the rest of the season.
“The Dutchman has close links at Stamford Bridge and is keen on using them to help bolster his squad ahead of the transfer deadline,” states the report in The Daily Mail.
Hasselbaink played for Chelsea from 2000 to 2004 and is very popular among the fans. The Dutchman was recently appointed the QPR manager, and it seems that he wants to make the most of his links with the Blues.
Bamford is a good striker and has proved himself in the Championship. The 22-year-old scored 16 goals and 28 chances in 40 Championship games for Middlesbrough during his loan spell last season.
The youngster was loaned out to Crystal Palace at the start of the 2015-16 campaign, but he struggled to make an impact at Selhurst Park.
The England Under-21 international could manage to make just six appearances in the Premier League for the Eagles, failing to score a single goal and created just two chances.
QPR have recently sold Charlie Austin to Southampton, and Bamford could prove to be an able replacement for the 26-year-old English striker.
Other interested clubs
QPR are not the only club who have been linked with a move for Bamford in the January transfer window.
HITC Sport reported earlier this month that Norwich City and Swansea City are interested in the youngster.