Limpopo human settlements MEC Clifford Motsepe appeared to try bribe a City Press reporter, the newspaper reported on Sunday.
Motsepe offered the newspaper's Limpopo correspondent Sipho Masondo a "wad of cash" on Friday, according to the report.
Motsepe on Saturday denied offering Masondo any money and questioned the journalist's integrity.
His lawyers on Saturday night demanded that City Press not run the story, the newspaper reported.
Following a week which saw Motsepe have to fend off damaging media reports, he invited Masondo to his house on Friday morning.
The Star newspaper reported that tender documents were allegedly tampered with to award R900-million housing contracts to companies owned by friends of former ANC Youth League president Julius Malema.
According to City Press, Masondo had given his version of events in an affidavit signed under oath.
After the meeting which lasted 30 minutes the two walked to the front door.
"There, Mr Motsepe reached into his pocket and took out a wad of cash, neatly held together with an elastic band. He held it out to me and said something like 'this is for petrol for the weekend'," City Press quoted from Masondo's affidavit.
"I told him I could not accept the money. I noticed that it was a substantial amount of money. I could see there were R100 and R200 notes. the notes looked crisp and fresh."
Masondo said the MEC tried to persuade him.
According to Motsepe all he said was: "Should he [Masondo] need any help from us as comrades in the province, he can come to me. Unless he misinterpreted that somehow."