Barca have long been linked with a move for the 19-year-old and recent reports claimed that the Spanish champions had beaten United and Liverpool to the Netherlands international.
However, according to Cataluyna Radio, United are prepared to pay De Ligt a bigger salary and also match agent Mino Raiola's own demands in an attempt to beat Barca to the centre-back.
The same report has claimed that the 20-time English champions are 'economically more committed' to the deal.
De Ligt captained Ajax to a league and cup double during the 2018-19 campaign, in addition to playing a key role as the Dutch giants reached the semi-finals of the Champions League.
United are expected to move for at least one new centre-back this summer after conceding 54 goals during the 2018-19 Premier League season.