According to the Express & Star, Wolves boss Kenny Jackett is interested in adding the youngster to his squad, as the west-midland side look to push for back-to-back promotions.
The 20-year-old is currently at Chelsea's pre-season training camp in Austria, and notched a goal in their 5-0 friendly win over Wycombe last Wednesday.
Wolves will face competition from Derby County, who want Bamford to rejoin them after a successful loan spell at the back-end of last season.
He scored eight goals in 21 appearances for the Rams helping them reach the Championship play-off finals.
Jose Mourinho is reportedly keen for the young striker to gain experience in the Premier League which could cast doubt over a potential move to either Wolves or Derby.
Premier League new boys QPR and Burnley have both been credited with an interest.
Bamford came through the youth ranks at Nottingham Forest after signing for them as a eight-year-old. He made two appearances for the Forest first team, both times coming on as a late substitute, but failed to score in either appearance.
When his promise became known in 2012 Chelsea signed him for £1.5 million. In the following campaign he was then sent on a season-long loan to MK Dons, where he scored four in 14 appearances.
Bamford went back to MK for the first half of the 2013/14 season and was even better, scoring 17 in 30 appearances. Once his loan deal with the Dons expired he moved to Championship side Derby.