Paladini left QPR in 2011, following the takeover by Tony Fernandes, and has previously been linked with moves for Birmingham and Millwall.
Lawn told the Telegraph and Argus: "We have signed a confidentiality undertaking and we are talking to him."
Bradford said when contacted by Press Association Sport they would not comment on media reports.
Paladini's previous attempt at a takeover was reported to be at Millwall, but chairman John Berylson played those down in January 2014.
Berylson said: "I have absolutely no interest in selling Millwall to Mr Paladini, who I have never even met nor have any intention of meeting, or anyone else."
Bradford are currently 11th in the Sky Bet League One table following Tuesday's 6-0 thrashing at the hands of Bristol City, which sealed the Robins' promotion to the Championship.
Source : PA