The Iceland playmaker is in his second spell with the Swans, and such is the 27-year-old's imperious form, that Bradley accepts other clubs will be looking at him.
Sigurdsson's market value is likely to be £20million or more, but Bradley has underlined his importance ahead of Wednesday's Premier League clash against West Brom at The Hawthorns
"Gylfi has been terrific for us," Bradley said.
"I am sure there are many clubs that are taking notice
But certainly from our standpoint, we consider him important as we move forward.
"We are confident he is going to still be a part of our team as we get into the second half of the season and beyond.
"For us to not only improve week to week, but have a little bit of a longer-term vision of how we can improve and how we can move ourselves forward, a player like Gylfi is a vital part of that vision.
"I believe that he is going to be with us
All you have to do is look around football, and sometimes crazy things happen, but there is no sense getting too deep into that conversation right now.
"On the inside of our football club, we are confident he is going to be part of our team moving forward
We all feel very good about what he is doing for us on the field."
Swansea are likely to be active in the January window, and Bradley admitted that Tottenham's England Under-21 international Tom Carroll - a former Liberty Stadium loan player - had been discussed.
"You get different names out on the table, and then there are discussions about which ones fit the best and which ones have the greatest chance to happen," Bradley added
"Transfer windows aren't always easy to plan out every detail
Things change quickly.
"The starting point is making sure we've got good names and we've done our research
A lot goes into it, and I think we are looking at some interesting possibilities, and now we keep our fingers crossed.
"Tom is a player that everyone here knows
He is certainly a good footballer, and he is a player that has been discussed
Tom is tactically sharp and he is a good passer, which are qualities that a team can use."
Swansea remain in the Premier League's relegation zone, but a 3-0 victory over Sunderland last weekend means they will travel to the Midlands targeting another success that would make it back-to-back league wins for the first time this season.
"Building on a good game and turning it into another good effort, trying to put a run together, these are very important parts of growing as a team," Bradley said.
"West Brom are a good solid team
Tony's (Pulis') teams are hard to break down, they are direct and there is a physical part of their game.
"They are impressive in terms of their team shape and how they go about their business every game.
"His record speaks for itself
He deserves respect
If you go around the Premier League, not everyone has the same ideas on football, but also what needs to be said is that not everyone has the same players.
"One of the things a top manager understands, and I say this about Tony, is how to get the best out of his team, and so his understanding of what his players are all about and to put them on the field and get them organised in a way that gives them a chance for results.
"There are different ways to do it, but ultimately that's what all managers are trying to do."
Source : PA