The Swans are currently sat in 14th spot in the Premier League table, having taken 14 points from their opening 13 games, and are five points clear of the relegation zone.
A league run which has seen the side win just the one of their last nine league games has led to reports that manager Garry Monk's job is under threat, but Ayew is quoted in the South Wales Evening Post as saying that he is confident fortunes will improve over the coming weeks.
The Frenchman said: "The manager has shown us a lot of support, a lot of confidence, and we're trying to give it back to him on the pitch.
"He's a great manager, we know what he did last season. Everything's going to get back into shape.
"Sometimes in football things are a bit difficult, but I believe we have great players, a great manager and a great squad so everything will be okay. We just need to keep working hard and not give up."
The side have got a tricky run of games coming up, which starts when they travel to a confident Liverpool side at Anfield on Sunday.
From there, they face the league's current leaders in Leicester City before testing fixtures against Manchester City, West Ham United, West Bromwich Albion and Crystal Palace wrap up the calendar year.
There is an obvious need for the side to get a decent points haul during this run to ease the fears surrounding Monk's future, as well as any relegation concerns.
Ayew says they will head to Anfield with confidence, and a good result there will give them and the manager a timely boost heading towards the busy festive period.