The Reds ideally wanted a permanent deal for the 23-year-old this summer but, despite interest from Burnley, the £20million asking price proved too high.
With little chance of first-team football, the PA news agency understands Liverpool have now reconsidered their stance.
Although the likes of Swansea, Norwich, Derby – where Wilson spent a previous loan spell – and Nottingham Forest were in the running, Cardiff are the only ones to meet the financial package which includes a £1.2m loan fee and covering his full wages.
The Wales international has made just two first-team appearances, a third-round FA Cup replay at Plymouth in January 2017 and in the Carabao Cup penalty shoot-out defeat to Arsenal earlier this month.
He spent a successful loan spell at Bournemouth last season.
