The Gunners are ready to let the young Northern Ireland international depart permanently, per the Daily Mail.
He will move in a £2 million deal, while Arsenal will also include a sell-on clause and matching sale price clause within the agreement.
Ballard would be new Burnley boss Vincent Kompany's first signing if the move goes through.
He would go some way towards replacing departing centre-backs Ben Mee and James Tarkowski.
Ballard has never played competitively for Arsenal, but managed 33 appearances for Millwall in the Championship on loan last term.
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