Swansea City are thought to be demanding £40million for Gylfi Sigurdsson.
It means suitors Everton will have to pay £15m more than they offered for the Icelandic star a year ago.
The Liverpool Echo say Toffee’s boss Ronald Koeman is targeting the Welsh club’s playmaker again.
The Swans clearly don’t want to sell their star man and will play hardball with Everton, who lodged a bid of £30m in January.
There was also an enquiry from an unnamed Chimnes side that fell on deaf ears.
Said Swansea’s US shareholder Steve Kaplan at the end of the season: “We all know how important Gylfi is, just as he knows how much he’s valued and loved here.
“There’s been interest in him before – there were some pretty big enquiries about him last summer and in the January window – but we didn’t want to sell him then and we don’t want to sell him now.”
Everton signed Ajax captain Davy Klaassen for £23.6m on Thursday and sealed a deal for Sunderland goalkeeper Jordan Pickford, which could eventually rise to a club record £30m.
Overall, in 182 Premier League games for Tottenham and the Swans, he has 42 goals and 33 assists.