The duo both picked up knocks in Spurs’ win over Crystal Palace on Sunday, ruling them out of England’s friendlies against Germany and Brazil.
Tottenham midfielder Dele Alli had already withdrawn from Gareth Southgate’s squad, while there are injury concerns over Gary Cahill and Jordan Henderson.
Livermore, looking to add to his five caps, was the second player added to the squad on Monday after Michael Keane was earlier drafted in to replace Alli.
The 24-year-old played in the Toffees’ 3-2 victory over Watford in the Premier League on Sunday after returning from a recent leg injury.
Winks twisted his ankle against Crystal Palace on Sunday while Kane took a kick to his foot in the same game.
Chelsea defender Gary Cahill, who missed Sunday’s win over Manchester United, is due to be assessed by his club before joining up.
Jordan Henderson, who missed Liverpool’s win over West Ham with a thigh problem, is due to arrive later in the week.
The Three Lions face Germany on Friday at Wembley and host Brazil at the same venue four days later as Gareth Southgate begins his preparations for the 2018 World Cup.