Under the plan, a new team would be formed with a new name and would take Bridgend's place in the Welsh Premiership, which would require approval from the Welsh Rugby Union.
King confirmed that the possibility of a merger had been raised with the WRU.
"The WRU seemed okay about it," he said. "It would give them a bigger club in the Premier division and I don't think we would have any problems with them."
Bridgend have produced some of the sport's biggest names such as JPR Williams, Gareth Thomas and Robert Howley, while Gavin Henson went to school in the town.
The club does not own its Brewery Field ground, but is guaranteed to play there for the next five years under an agreement with Celtic Crusaders.
Maesteg's best-known ex-players include Wales and Lions backs Allan Bateman, Gwyn Evans, Mike Hall and Chico Hopkins.
The two clubs have been bitter local rivals for more than 130 years and it is likely a merger would divide opinion among the clubs' supporters as well as raising questions from other clubs in the Premier division.
We now recognise that in this borough rugby union has a problem and that we have a real fight on our hands
Bridgend chairman Derrick King
Those questions will almost certainly be aired at a meeting of the Premier Clubs in Aberavon on Tuesday night.
WRU group chief executive Roger Lewis will attend, with clubs concerned about plans for a fifth regional side and what they perceive as a delay in implementing measures from last April's Premiership review.
There is still ill-feeling in the Bridgend area over the closure of the Celtic Warriors regional side five years ago, with many fans feeling disenfranchised, despite the efforts of the Ospreys, who now have regional responsibility for Bridgend and Maesteg.
"The Celtic Crusaders have taken advantage of the gap," said King. "We now recognise that in this borough rugby union has a problem and that we have a real fight on our hands."
The four Welsh rugby union regions have already discussed the threat posed by Super League, which has the potential to affect the Ospreys and Blues in particular and Gill had another warning for the rest of Welsh game.
"A lot of people have always believed that rugby league would never work in South Wales, but this is a powerful thing with a lot of money behind it.
"There would be a lot of face to lose if it were to go wrong, so people will make it work."
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