According to The Sun, the player is deemed surplus to requirements under manager Antonio Conte.
Winks, 26, has been on the fringes of the Spurs squad since the arrival of the Italian manager in November.
He has been with his boyhood club since the age of five, but the north London side are now prepared to let him leave, should a club cough up in the region of £20million.
Sevilla are prepared to offer him an escape route and keen to help him resurrect his career in a league where his technical ability is suited.
Winks has made over 200 appearances for Spurs, and also featured in the 2019 Champions League final under former boss Mauricio Pochettino.
Playing regularly in Spain will no doubt boost Winks' England chances.
With 10 caps so far for his country, he will be keen to impress Three Lions boss Gareth Southgate ahead of the World Cup in Qatar later this year.
Winks fell down the pecking order at his current club, with both Pierre-Emile Hojbjerg and January signing Rodrigo Bentancur ahead of him right now.
Oliver Skipp is another who is preferred over Winks, and Conte is likely to want another addition too, so a move away is likely to benefit all parties, despite his contract running until the summer of 2024.
According to the report, Everton, Fulham, Southampton and Newcastle have also been keeping tabs on the player.
Tottenham are said to be keen to offload several stars as Conte looks to shape his squad ahead of next season.
Tanguy Ndombele, Bryan Gil and Giovani Lo Celso, who all spent the second half of the campaign on loan, are expected to leave.
Meanwhile. the futures of Steven Bergwijn, Sergio Reguilon and Joe Rodon remain up in the air, and the trio could also be sold at the right price.