The Swans forward has been on the radar of a host of Championship clubs this summer as he entered the final 12 months of his contract.
The Whites made him a priority target in recent days as they have been looking to add a Championship-proven goal-getter to their squad.
Even though Leeds submitted an offer to Swansea for Piroe, agreeing personal terms with him was claimed to be a stumbling block for the Elland Road outfit.
However, Leeds have agreed a fee with Swansea and are now red hot favourites to complete the capture.
According to Dutch daily the Eindhovens Dagblad, Piroe’s former club PSV Eindhoven will be getting a €4m cash windfall from the move.
Piroe came through the youth set-up at the Dutch giants, who are currently battling Rangers for a spot in the Champions League group stage, before leaving for Swansea in 2021.
Leeds will be looking for Piroe to score the goals to fire them straight back up to the Premier League this term.