Shortly after guiding the serial strugglers to safety, Allardyce had said he was determined to have a good close-season recruitment in order to avoid flirting with relegation for a fifth consecutive campaign.
"We need two, three or four players as quickly as we possibly can. It's been a huge demand on all our resources trying to find those players and we will continue to until we're successful," Allardyce told British media.
"The fans, hopefully, will be a little bit patient. I have to admit myself that my patience is wearing thin - very, very thin indeed - but we have to keep striving to bring in those three or four players as quickly as possible."
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With the Premier League's 5.14 billion pound ($6.72 billion) domestic television rights deal set to kick in from August, Allardyce felt players were being overpriced in the market.
"The same player that cost 10 million pounds last year will now cost 20 million... and the 40 million ones now costs 60 million or 80 million," added the 61-year-old, who has been linked with the vacant England job by the British media.
"That is the unfortunate market that we are working in, and we are trying to work in that market as shrewdly as possible to get the best players and the best value for money as we can."
Sunderland will begin their Premier League season with a trip to Pep Guardiola's Manchester City on Aug. 13.
($1 = 0.7653 pounds)
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Amlan Chakraborty)
