According to the Seville daily ABC, the former Brighton and Hove Albion, Sunderland and AEK Athens coach flew to London on Thursday after taking his last training session with the struggling Andalusian side.
Betis have taken 11 points from 11 games under the Uruguayan and are 14th in La Liga, two points above the relegation zone.
A former midfielder for Uruguay, Real Zaragoza, Chelsea and Tottenham Hotspur, Poyet succeeded Juan Merino at Betis but got off to a nightmare start, losing his first game 6-2 to champions Barcelona.
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His fortunes improved as Betis took eight points from their next five games but a downward spiral began with a 1-0 defeat at Real Sociedad, the start of four defeats in five matches including a 6-1 thrashing at home by Real Madrid.
Poyet has also been criticised for leaving talisman Ruben Castro, the team's top scorer last season, out of his starting lineup for two of the last three games.
Betis are one of the best supported clubs in Spain and one of only nine teams to have won La Liga.
In recent years they have witnessed upheaval on and off the pitch, suffering relegation in 2009 and 2014.
Poyet is their sixth managerial appointment in three years. Former Levante and Getafe coach Luis Garcia Plaza is the favourite to replace him if his sacking is confirmed.
(Editing by Tony Jimenez)
