The Blues may be more open to releasing one of their own attackers, or less interested in the other strikers on the market this summer.
Chelsea completed the long rumoured loan signing of former Manchester United striker Radamel Falcao recently from Monaco, and it could be a move that has big consequences around the Premier League when it comes to signings.
The Colombian essentially replaces departed Blues legend Didier Drogba up front. It means Chelsea now have someone, if he returns to previous form, that is a real alternative up front to Diego Costa. Falcao can also play up top with his former Atletico Madrid strike partner.
Depending on how many strikers Jose Mourinho will be looking to have on his books next season, and last year he went with the three first team forwards, that could mean that at least one of the club's other attackers will be available to any interested parties.
The Frenchman may feel that Falcao's arrival puts him even further away from the Blues' first team, while Bamford may be eager for regular Premier League football if he can get it.
Falcao's signing could also mean the end of the club's interest in Charlie Austin, which would of course be a great relief to the other club's tracking the QPR forward. If Chelsea really wanted the 26-year-old, there aren't many clubs that could stop the West Londoners, but with the champions less desperate for attacking reinforcements, the Baggies and Palace, who are also considering Austin, along with Newcastle as stated in the Birmingham Mail, may be in with a stronger shout.