Gylfi Sigurdsson has been hailed as the man who turned Swansea City around last season as the club ponder what to do about Ashley Williams.

The Swans rejected a bid of £10m for Williams from Everton on Tuesday night but are expected to be presented with an increased offer for their captain.

A higher bid for Williams, who turns 32 this month, could yet tempt Swansea to cash in – in contrast to their determination to keep Sigurdsson, who has signed a new four-year contract.

The Icelandic midfielder – who, like Williams, enjoyed a highly successful Euro 2016 campaign – was the key man last season in pulling the Swans away from the relegation zone, according to head coach Alan Curtis.

“He was so instrumental last season, especially when we really needed results,” said Curtis.

“Gylfi stepped up to the plate and scored some crucial goals when we needed them most.

“Everybody contributed, especially as we finished the season quite strongly, but during that difficult period we had, Gylfi was hugely prominent.

“We are all delighted that he has put pen to paper on a new contract because he will be a key player for us over the next few seasons. It’s a lift for us all.”

Sigurdsson scored 11 goals in 36 appearances last season before helping Iceland knock England out of the Euros on their way to reaching the last eight.

The 26-year-old was understood to be a £25m target for a number of clubs, but having spent a mixed short spell at Tottenham between 2012 and 2014, he has opted to remain at the Liberty Stadium.

“Gylfi showed what he can do in the Euros,” added Curtis. “Iceland did extremely well and I thought a lot of that was down to Gylfi.

“It’s not just his general play, it’s the ground he covers, the goal threat he brings and also his dead-ball expertise.

“Set-plays are a huge part of the game these days and it’s no coincidence that he is just about the last off the pitch in every training session.

“He stays behind do to extra work on his technique and you see that on a Saturday. All credit to him for that.”