Seven-time world champion Hamilton is leaving Mercedes for Ferrari at the end of this season and media reports have put Albon high on the list of potential candidates to replace the Briton.
Speaking to reporters by video conference after the team's livery launch in New York on Monday, Vowles clarified Albon's current contract situation.
"Alex is signed in Williams until the end of 2025, that's signed," he said.
"It's not something I've been very public about because I don't feel the need to. So any reports that you are seeing... they are speculating at best.
"As I've also said publicly, it is our job in Williams to create an environment that deserves someone of the calibre of Alex," added Vowles, who joined the Mercedes-powered team from Mercedes a year ago.
"He is an incredible driver that deserves his place towards the front.
"We put him in difficult positions and he overcame that to score points. He and I have good chats about where we want to move forward... we want to have our journey together in this team for a long time."
Albon scored all but one of the team's points last season, lifting the former champions from last place in the standings to seventh overall.
The British-born Thai also outqualified his US rookie teammate Logan Sargeant (23) 22-0.
Asked if his deal was set in stone, Albon sounded less certain but said his focus was on 2024. "Let's see. Time will tell," he replied.
"Realistically, I want to be with the team. If the team is where I want it to be, it will be a long-term contract."
