Tony Pulis is chasing up to five more signings before the end of the month after landing Matthew Upson on Tuesday, with Palacios and Crouch at the top of his shopping list.
Both players are long-time targets of Stoke's and Coates confirmed to Radio Stoke on Tuesday evening that a final bid had been made to Spurs.
He told BBC Radio Stoke: "We've made our last bid. The ball is in their court. We shall not be negotiating from where we are.
"The last conversation I had with Spurs, we had not agreed anything. We'll see what happens, but we haven't got any further."
It has been reported the north London club want £20million for the pair, but the Potters are unwilling to meet that valuation and may also ask for their wages to be subsidised.
However, Stoke are privately confident of landing at least one of their targets with Spurs keen to trim their squad to fund their own summer transfer business.
England forward Crouch, 30, began his career at White Hart Lane as a trainee and returned to the club two years ago for a reported fee of around £9million after spells with sides including QPR, Portsmouth, Aston Villa, Southampton and Liverpool.
He scored 11 goals in 45 appearances in all competitions for Harry Redknapp's side last term, having netted the winner at Manchester City in May 2010 to secure fourth place for Spurs in the Premier League.
Honduras midfielder Palacios, 27, joined Tottenham in January 2009 in a £12million transfer from Wigan. He had moved to the north-west of England from Honduran club Olimpia after a brief loan spell with Birmingham.
Upson, meanwhile, says he is relishing the fight for places at the Britannia Stadium. He joins Robert Huth, Ryan Shawcross and Jonathan Woodgate at the club but feels the competition will help them all.
"There is a lot of competition for places here and that is part of the attraction," he told the club's official website.
"I will relish the fight for a spot because it draws the best out of players."