Andrew Neil could reportedly return to the BBC at some point in the future following his acrimonious exit from GB News last month.
The 72-year-old left the BBC last November in order to take up a new post as chairman and lead presenter of GB News, which launched in June.
Neil confirmed his departure from the channel last month having presented just two weeks of his flagship show, citing serious disagreements with management over the editorial direction of the broadcaster.
The veteran journalist also left the BBC due to a disagreement - albeit a significantly minor one - after executives signalled their intent to move his primetime BBC Two show into daytime.
The newspaper says that there are no suggestions that Neil could return to the broadcaster imminently, but the talks "served to build bridges" as Davie was keen to check on Neil's wellbeing.
The news comes days after it also emerged that BBC political editor Laura Kuenssberg is looking to leave the role for a new job on Radio 4's Today programme.