Everton have seen a £27 million bid for Swansea midfielder Gylfi Sigurdsson rejected, sources close to the Welsh club have told ESPN FC.
Sigurdsson, 27, scored nine goals and handed 13 assists to teammates as he helped Swansea beat relegation last season.
However, Everton and his former side Tottenham have both been strongly linked with a move for the Iceland international and reports suggest that he may be tempted by the prospect of playing European football.
Sources told ESPN FC that Everton have now made their move but that Swansea have rejected their first offer.
Sigurdsson signed a new four-year contract last summer and Swansea chairman Huw Jenkins revealed in February that he had been the subject of "substantial offers" during the last transfer window.
The midfielder himself said last month that he was not planning to leave the club unless they wanted to sell him.
"I signed a new contract in the summer and I've got three years left," Sigurdsson told reporters. "So it's down to the club if they want to sell me. But I was very happy when I was on loan here and then again in the last three years.
"I'm not trying to leave, I'm not desperate to go or anything."