Key player out of Leeds United's Championship play-off final
The striker has not played since injuring his knee against former club Middlesbrough at the end of the regular season.
Bamford has started 15 Championship games this season, scoring eight times.
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Hide AdWithout him, Joel Piroe is likely to lead the line against the Saints at Wembley.
"Patrick is not available, he won't be there," said Farke. "He will definitely miss out."
That apart, the injury news is positive, with no fresh injury concerns after the 4-0 second-leg win over Norwich City which booked Leeds' place at Wembley.
"We had some minor issues during this week but it seems like every player (concerned) will be available," said Farke.
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"Sam Byram after his injury in the last game returned to team training on Thursday and if his body doesn't show any reaction he will be available for this game.
"Apart from our long-term injuries, Pascal Struijk and Stuart Dallas – and Patrick Bamford – the others are available."
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