The 21-year-old, crowned Championship player of the year on Sunday, has been superb on a season-long loan at promotion-chasing Middlesbrough this term, scoring 19 goals in 41 appearances.
Bamford has spent the past three seasons on loan in the lower divisions, playing for MK Dons between November 2012 and January 2014 and then Derby at the end of last season.
The England U21 international has a year left on his current deal at Stamford Bridge and he warned the Blues of his reluctance to sit on the bench next term.
“I want to play for Chelsea, I hope I do get that chance and I think I can compete,” he said.
“A lot of people said I left Nottingham Forest for the wrong reasons, but that wasn’t true. I wanted to play for a top team like Chelsea.
“However, after two years regularly playing out on loan, going back and sitting on the bench wouldn’t really help me.
“So it’s down to those at the top at Chelsea to decide what will be the best for my career and what to do next year.”
Bamford joined Chelsea from Forest in January 2012 but has never made a first-team appearance, instead scoring 21 goals in 44 appearances for MK Dons.
He then bagged eight in 21 for Derby as they reached the Championship play-off final last season.