The Sunday Mirror says United's bid to sign the hugely talented Zaha is on the brink of collapse.
Palace chairman Steve Parish met with United officials on Thursday to hear their latest offer.
But the Eagles, having already slashed £5million off their original £20m valuation for the England international, were not willing to do business.
United are expected to resurrect a move for the 20-year-old in the summer.
Arsenal have not firmed up their interest with an official bid – and a Gunners offer could prompt United to return to the negotiating table.