The Chile international is rumoured to have been offered wages of more than £500,000 a week to choose United over fellow interested clubs Chelsea and Manchester City.
Over the course of a four-and-a-half-year deal that is worth £118.3m, which Burnley boss Dyche believes may have a trickle-down effect on teams further down the transfer food chain.
"It creates a tougher challenge because every time one of the superpowers spends enormous money on a player that drip-feeds down the market," he told reporters at his weekly press conference.
"So every player you then phone about has miraculously gone considerably up in value because they'll say 'well if he's worth that our players must be somewhere near as good as that'.
"So where does the next move from us come from? Where's the next valuation on one of our players or one of our targets?"
Burnley, currently five points behind Arsenal in seventh place, take on Man United at Turf Moor on Saturday afternoon.