The Northern Ireland international was acclaimed by his country’s manager Michael O’Neil as the best player on the pitch on Tuesday night, after his team drew 1-1 with Wales.
Galbraith has also been one of his club’s most consistent performers in the Championship this season and along with top scorer Zan Vipotnik is Swansea’s most valuable asset.
The 24-year-old still has two years to run on his current contract - with the option of a third - following his £1.5m move from Leyton Orient last summer.
But aware there is likely to be interest in Galbraith from other clubs this summer, the Swans are also considering an improved deal for the player.
“I never speak about contracts here until after we have signed them,” said Matos.
“Contracts, or future signings, or transfers - it's something that we do it internally, so let's see.”
But when asked whether he would like to tie down Galbraith on a long-term deal, Matos added: ““I think he's a player we want to see in Swansea for the next 10 years, so let's see how long we can sign the contract.
“But 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.
“So, 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 has already played 44 matches for Swansea this season, often used as a right back as well as in midfield.
His comfort in possession, neat skills and range of passing has quickly made him arguably the most influential player in the team and the former Manchester United youngster earned rich praise from O’Neil for his displays against both Wales and Italy, who ended Nothern Ireland’s World Cup ambitions in the play-off semi-final last week.
"He made a really good choice in the club he went to," O'Neill said of Galbraith’s decision to join the Swans.
"I spoke to him in the summer and he had other options. I think relocating to Swansea was maybe not at the top of his list because he has been in London and Manchester for the majority of his career.
"I've known Ethan since he was 15, 16 years of age, when he was in our age-grade and development squads.
"It took him longer to come through maybe than what we'd hoped and part of that is obviously his development with his club.
"But I think over this season, the player we always knew [was there has come through]."
O'Neill says there is more to come from Galbraith, who has the ability to develop into a "top-class player".
"I think where he has improved is physically in the Championship," he added.
"He's able to compete, he covers the ground, his physical data is high, but it's his ability to retain the ball - his technical level is extremely high.
"For me, his best position is definitely in midfield in our team."
Galbraith, however, may be missing when Matos’s men resume their Championship campaign away at Sheffield United on Friday, due to a calf injury picked up at the Cardiff City Stadium on Tuesday night.
Swansea will definitely be without defender Josh Key for their trip to the Blades, who lay three places and two points behind Swansea in 17th position.
