It was a first half of few opportunities at the Liberty Stadium as Swansea City and Everton went into the break goalless.
With six minutes gone, City striker Danny Graham beat the offside trap but his weak shot from the edge of the area was saved comfortably by Tim Howard.
Gylfi Sigurdsson, looking to continue his fine goalscoring record since joining the Swans on loan in January, also tried his luck from 18 yards but shot wide.
With a win, Everton would go above Swansea in the table while three points for Brendan Rodgers's side could go level on points with the Toffees' Merseyside rivals Liverpool.
