Summer signing Dobbie has struggled for first team chances, with Paulo Sousa usually preferring a more physical style of striker to lead the line up front.
A deal for Britton, whose contract expires at the end of the season, was widely expected to be completed in the final few days of the transfer window, with Wigan the most likely destination.
However, it seems that the midfielder will at least be staying at the Liberty Stadium until July, along with Spanish full back Angel Rangel, also tipped for a January exit.
Rangel, who is set to trigger a contract extension by playing this weekend, has been linked with moves to Wigan and Celtic but a deal never materialised, and the full back will remain at the club, for now.
Meanwhile, former Man City youngster Scott Evans is the other to leave – on a free transfer.
