England global Kane will undergo a scan on Monday having picked up the problem scoring a disallowed goal at the Vitality Stadium.
Spurs face Swansea in their FA Cup quarter-final on Saturday, while England play the Netherlands and Italy in friendlies later this month.
Spurs' prolific Harry Kane was looking to snap a mini-goal drought after firing blanks against Huddersfield and Juventus.
Tottenham Hotspur manager Mauricio Pochettino admitted he can only wait and hope an ankle injury suffered by talismanic striker Harry Kane isn't serious. We hope as quickly as possible he can recover and be available.
"He felt that when he ran and twisted his ankle that it was impossible to stay on the pitch".
Spurs would go on to win the match 4-1, but the victory could prove costly.
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The England global is due to have a scan tomorrow to determine the full extent of the injury so Tottenham will be praying for positive news when the results come back.
Speaking about Alli, Pochettino added: "I don't believe that it's a big issue".
"Look, in football you need always some luck because the decision should be different, maybe now we are talking in a different way, but that is football, it happened Wednesday [against Juventus], happened the week before, but I accept football is like this. But I don't believe it will be a big issue".
Tottenham are in fourth place in the Premier League table and five points clear of Chelsea FC, who lead the chasing pack.
"I think he is having a fantastic season, the best season since he arrived".
"The Cherries were denied victory by Riyad Mahrez's 97th-minute equaliser for Leicester last week but I don't think they will find themselves in a similar position this time around".
Bournemouth, who remain 12th, though they had rescued a point via Callum Wilson's 84th-minute strike but referee Mike Dean disallowed it for a shove on Spurs defender Davinson Sanchez, before the visitors scored their two late goals.
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