The Three Lions captain was hurt in a freak collision with a goalpost during Bayern Munich’s 5-2 victory at Darmstadt on Saturday.
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Kane, 30, will join up with Gareth Southgate’s squad at St George’s Park ahead of friendlies against Brazil and Belgium despite limping off in the Bundesliga game.
While it is hoped his twisted left ankle is not too serious, he is far from certain of facing Brazil at Wembley on Saturday.
Bayern Munich sporting director Christoph Freund said: “Harry will be looked at in England.
“He has trusted doctors there. We are in close co-ordination on this. Harry won’t take any risks.”
England’s all-time scorer had netted his 31st goal of the season for Bayern just before half-time.
It meant the ex-Spurs forward set a new record for a player in their first Bundesliga season, beating Uwe Seeler’s 30 for Hamburg in 1963-64.
The striker is on target to break Robert Lewandowski’s record of 41 goals in Germany’s top flight — set while playing for Bayern in 2020-21.
And his club will be desperate for Kane to be fit for next month’s Champions League quarter-final showdown with Arsenal.
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Meanwhile, Sasa Lukic fired a warning shot to England ahead of their Euros 2024 showdown with Serbia after dealing with James Maddison in a “dress rehearsal”.
Fulham’s midfield enforcer, 27, got the better of Tottenham’s No 10 in a 3-0 home win at Craven Cottage.
Lukic will hope to replicate that combative form for the Serbs against the Three Lions in the European Championship Group C opener in Gelsenkirchen on June 16.
And when asked if he was relishing taking on Jude Bellingham & Co in Germany, Lukic’s face lit up.
Lukic, who has won 42 international caps, said: “Yeah, I can’t wait.
“Today was like a dress rehearsal because Maddison was there and it’s definitely going to be a good game against England at the Euros.
“I’m proud to be Serbian and play for my country. We are in the Euros for the first time in our history and I hope to do well.”
Lukic scored his first goal in English football since moving over from Serie A side Torino for £8million in January 2023 but the vital deflection from a cross came off his KNEE.
He laughed: “It was my knee, it was strange, but it’s important to score a goal. I hope to score many goals for Fulham.
“This was my fourth game in a row. Prior to that, I didn’t play much.
“It was hard, it wasn’t an easy time. I worked a lot on myself.
“But it proved that with a performance like this — and the ones against Manchester United and Brighton — my work has been paying off.
“Do we feel unbeatable at home? Yes, of course we feel it. It’s really nice to play here because the fans are like our 12th man. We give everything for them.”
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