Former Northern Ireland midfielder Hughes scored the goal which kept Barnet in League Two in the 2-1 win over Burton on the final day of last season.
Versatile Deering scored three goals last term in 47 appearances after joining from Oxford.
New boss Mark Robson had already lost last season's top scorer Izale McLeod, whose contract had also run out, and said last week he expected Hughes to follow suit but had planned talks with Deering.
However, he has been unable to persuade him to stay and has some major rebuilding work over the summer.
