HITC Sport understands that the Chelsea striker would prefer another top-flight deal.
The 22-year-old has just returned from a unsuccessful loan stint at Crystal Palace, where he was meant to spend the full season but he and Chelsea opted to end the deal.
Bamford failed to start a single game during his stay at Selhurst Park, but he now has a number of teams already interested in landing him.
Chelsea's interim boss Guus Hiddink had been considering letting him stay at Stamford Bridge, and while he is set to link up with them in the coming week, another loan deal will be sanctioned.
Championship promotion favourites Middlesbrough, where Bamford spent last season and finished with 17 goals, would love to have him back and told Chelsea as early as November that they would take him, but a Premier League move appears more likely.