Matos says Galbraith has established himself as a “really important player” having made an “impact” whether playing in midfield or as a back-up right-back.
The player has quickly become one of Swansea’s biggest assets alongside striker Zan Vipotnik, who agreed a new long-term contract last month.
While Matos hopes Galbraith will follow Vipotnik by signing a fresh deal, he says the Swansea hierarchy must agree to make that happen.
“It needs to be a collective approach, something that is not only from me, but is something from the club because nowadays in football you can see that managers quite often come and go,” he added.
“I think in these kinds of situations the manager needs to have the first and the last word, but in the middle there’s a lot of discussion that happens where there needs to be a collective approach.”
Galbraith hopes to add to his 44 Swansea appearances when Matos’ side return to action at Sheffield United on Friday (15:00 BST).
However, his fitness for the Bramall Lane trip is being assessed after he returned from Northern Ireland duty complaining of a calf problem.
