The 28-year-old, who has recently helped his country reach the quarter-finals of Euro 2012, is available on a Bosman free transfer this summer after failing to agree a new contract with Turkish side Besiktas.
And, while Sevilla looked to be favourites to secure Sivok's signature after keeping tabs on him at the European Championship in Poland and Ukraine, Spanish newspaper Marca is now claiming that Fulham boss Martin Jol will look to hijack the move with a higher offer and take Sivok to Craven Cottage.
The report follows on from Sivok's agent Jiri Mueller's admission that they were due to hold talks with Sevilla, while Besiktas and an un-named English club, thought to be Southampton at the time, were also vying to sign him.
"We have opened official talks with Sevilla and would like to have things sorted out as soon as possible," said Mueller
"We also have registered interest from a club in the Premier League and Besiktas have come back into the race as they want to keep Tomas."