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Ten-man Chelsea beat Brighton & Hove Albion 3-2 at Stamford Bridge while fourth-placed Aston Villa needed a late Ollie Watkins goal to scrape a 2-2 draw at Bournemouth.
Venables guided England to the semifinals of the 1996 European Championship on home soil before losing to Germany on penalties.
The result left Spurs second in the standings behind Manchester City.
It was a triumphant return to Spurs for Mauricio Pochettino who got the biggest win of his short Chelsea tenure.
Manchester United's campaign of woe continued with a 1-0 home loss to Crystal Palace but there were no such troubles for Arsenal who, along with Spurs, closed the gap to leaders City to one point with a rampant 4-0 win at Bournemouth.
Liverpool won 3-1 while Arsenal were held 2-2 by Spurs.
Pape Sarr scored in a 2-0 win for Tottenham Hotspur.
Despite a stellar scoring record he failed to win any domestic or international titles with Spurs.
Bayern did not disclose the transfer fee, which media reports have put at around 100 million euros ($109 million). That would be a Bundesliga record.
Should it be completed, Kane's move would be the most expensive transfer in Bundesliga history with an expected fee of about 100 million euros.