The Swans find themselves 10 points clear of safety, after an impressive come-from-behind draw against Stoke City at the weekend.
The Icelandic playmaker scored in the Swans 2-2 draw at the Britannia on Saturday, but has warned his team against complacency:
"You never know how things will pan out. But at the moment we're not feeling too confident. I think we need a few more points and ideally probably one win would seal it."
The Welsh club have an incredibly tough run-in with a visit from Chelsea up next, followed by games against relegation rivals Newcastle United and league-leaders Leicester City.
Their last three games see a trip to Champions League chasing West Ham United sandwiched by two home games against Liverpool and Manchester City, and Sigurdsson says it is down to them to ensure their safety:
"There's going to be some crucial games in the next few weeks. It's down to us to make sure that we keep on going and try to pick up as many points as we can and make sure by 15 May we are safe."
Since the appointment of Italian Francesco Guidolin in January, Swansea have taken an impressive 18 points from 11 games, and their fans will be hoping they can guarantee their Premier League status sooner rather than later.
Sigurdsson has featured in every Premier League game for Swansea this season, scoring 10 goals from midfield.