Manager Mick McCarthy is keen to bring in defenders Roger Johnson and Matt Mills from Birmingham and Reading respectively.
But efforts to complete the moves have so far floundered and Moxey is threatening to pull out of any deals unless there is movement sooner rather than later.
Blues are looking in the region of £10million for Johnson and Reading in excess of £3million for Mills.
Moxey said: "We have got feelers out to a number of clubs - so we either start getting serious now or we move on.
"We are now telling clubs to make a decision.
"We need to get things done and what we're saying is 'if you don't want to do business, we'll forget it and move on."'
Moxey has been delighted to have secured midfielder Jamie O'Hara and goalkeeper Dorus de Vries from Tottenham and Swansea respectively but is eager to recruit more new faces.
He said: "We've done one deal for a high-class midfield player (O'Hara) who, from the vibe we're getting within the game, will be regarded as a very astute piece of business.
"We're also delighted to have signed a quality goalkeeper (De Vries) who will provide the right competition (for Wayne Hennessey).
"But we need to concentrate on other, more pressing areas now."