The Liga club are seeking forward recruits after selling star striker Carlos Bacca to Milan this summer.
Spaniard Llorente - who is also understood to be wanted by Arsenal and Manchester United - is fee to leave Juve.
But the Turin outfit are determined to make some money on the 6ft 5in forward signed on a free transfer from Bilbao in 2013.
Juventus want £10.5m for the Spain international, according to newspaper Mundo Deportivo, and won't budge from that figure.
It leaves Sevilla in an awkward position as Unai Emery prepares his side for the start of the Liga season.
But it is a boost for Premier League duo United and Arsenal, who are both trailing the ace.
Arsenal were said to have held talks with Llorente's agent over a switch last week.
Corriere dello Sport claim his representative flew to London to agree the deal.
However, it is also reported that United manager Louis van Gaal has Llorente down as his 'mystery striker'.
Van Gaal recently revealed he wanted to make a new signing that few were expecting and, with only three fit forwards on his books heading into the new season, Llorente was tipped to be that man.
It was also revealed today that Crystal Palace and Stoke are in for Llorente, who is unwanted in Turin following the summer signings of Paulo Dybala and Mario Mandzukic to play alongside Alvaro Morata.
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