The Sun says Swans are trying to wreck Sam Allardyce's Gudjohnsen reunion.
New West Ham United boss Allardyce is offering his former Bolton player a return to England in the Championship.
The move had looked cut and dried but now Premier League new boys Swansea want to sign Gudjohnsen.
His father Arnor said: "I can confirm that both Swansea and West Ham have now offered contracts to Eidur.
"He is looking at both the offers."