Mark McGhee has been repeatedly frustrated in his recruitment drive since being appointed manager this summer.
Amiens defender Reda Johnson looks set to be the latest player to snub the Dons, while loan moves for Plymouth Argyle pair Jim Paterson and Steven MacLean have already stalled because of the pair's wage demands.
Argyle are also the club likely to benefit from this latest episode, having reportedly agreed a fee for 21-year-old Johnson after he impressed in a trial against Morecambe on Saturday.
McGhee, whose first competitive game in charge is Thursday night's Europa League qualifier with Sigma Olomouc, has insisted he is happy with the first-team squad he inherited from Jimmy Calderwood.
However, he wants to add four players to it before the start of the Scottish Premier League season.
Amid reports McGhee is to hold talks with managing director Duncan Fraser and his director of football over his budget, Miller told the club's official website: "We tried to bring a couple of lads in on loan from a mid-table Championship side but, given these guys were on £3,500 and £5,000 per week, respectively, we simply cannot compete.
"Equally, while we will do everything we can to support Mark, we have to ensure Aberdeen Football Club is still around in the future and, let's be frank, there are top clubs whose long-term future is by no means a certainty.
"Much has been made of the players we've lost and while the absence of Scott Severin is a blow, injury meant that Jamie Smith hardly played last season while Lee Mair was not a regular starter.
"But, that said, we must remain positive. We have a new management team in place, the return of European football and a new season just around the corner and these are exciting times.
"However, it is, I believe, only right that the supporters have some idea as to the conditions we are having to operate within right now.
"There is money available to strengthen the squad and we will support Mark as much as we can to bring new players in. That has started with the signing of Stuart Nelson."
Fraser added: "Of course we will support Mark as much as we possibly can, that's a given.
"However, I do think it's important to perhaps spell out where Scottish football is at present.
"Prior to the collapse of Setanta, we were sitting with a television deal in place and a budget that we could operate within and one that allowed us to plan for the next three seasons.
"Now we are in a situation where we have to operate with an annual budget of £600,000 less than originally budgeted for next year that has the potential to rise to over £1million over the coming couple of years.
"Make no mistake, every SPL club is suffering right now and I do mean every club."