Miguel Herrera has been fired as Mexico coach following allegations that he punched a television reporter.
Former Arsenal midfielder Abou Diaby has rejected an offer to join West Brom in favour of finding a new club in France.
The Clarets finished the campaign having in fact made a loss of over £4m, but the Rodriguez deal ensured they ended the season in the black.
The Turf Moor club returned £3.16million, which the board say will be used to support recently-appointed manager Sean Dyche.
Joint-chairmen Mike Garlick and John Banaszkiewicz said in a statement to shareholders: "This player trading remains a cornerstone of how the club balances it books.
"Looking forward, now that the initial Premier League parachute payment period has ended, and the introduction of the Football League Financial Fair Play Rules, we need to continue to plan carefully for the future.
"Your board are true Clarets' fans and we are committed to supporting the team and the manager to give us the nest chance of achieving the success we all feel the club deserves."