The Portugal international is due to undergo a medical at Burnley ahead of signing terms.
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Luis will join Burnley on-loan with an option to buy - so long as he passes his medical.
Terms have been settled on a €2.5m loan fee with the permanent option set at €22.5m.
It's suggested Luis, 26, will mark Burnley's final incoming transfer of the summer market. Luis said farewell to Benfica fans after yesterday's match at FC Alverca.