Austin joined Sky Bet Championship rivals QPR last week for a fee believed to be between £2.25-4million.
Dyche is eager to replace him before the transfer window slams shut but admits he has been forced to alter his targets.
"We've got things going on behind the scenes," he told the Burnley Express.
"There will be a financial implication, some of the players we were looking at will have changed clubs and so won't be available, and some of those were in our market.
"Now it leaves a market where some are beyond our (budget). We need to shop wisely, keep our lines of communication open with a number of parties and see what we can build."