Spurs have lodged a bid of least £14m for Arsenal target Julio Baptista.
Arsenal have led the race for the 23-year-old Brazil striker, but had a £13.75m offer rejected by Sevilla.
But a statement on Sevilla's official website said: "The most important offer that we have received is that of Tottenham, of more than 20m Euros."
President Jose Maria Del Nido said: "Time is passing by and there are fewer days in order for clubs to make higher offers than what we have received."
Spurs' reported move will stun Arsenal, who must now decide whether to increase their own offer after receiving more than £13m from Juventus for captain Patrick Vieira.
Arsenal boss Arsene Wenger, meanwhile, has hit back after Sevilla threatened to report Arsenal to world governing body Fifa for allegedly making an illegal approach to Baptista.
Sevilla were angry after Baptista revealed he had held talks with Wenger, even though a bid had been rejected.
Wenger said: "We approached Sevilla first. At some stage you have to speak to the player.
"You do it because you have to know if the player wants to join you."
Wenger was quoted in The Times newspaper saying: "When you're close to ending negotiations with the club, you have to know if you have to put a million more in."