The latest package, worth up to £600k, was recently turned down by Preston but Leeds are still keen to bring in a striker and may look to Healy for free next summer or turn their attention elsewhere.
Blackwell has stated the club's latest offer is still available to Preston.
"At the moment, we do not intend increasing the bid," said Blackwell.
"It is still there for Preston to look at and we feel it is very fair. It is still dragging on and we have to start looking at other players."