While a full agreement has not yet been finalised, the La Liga champions are hoping to announce the Netherlands international in the coming days.
The defender has been linked to a move away from the Champions League semi-finalist with Barcelona mooted as the most likely option, following team-mate Frenkie de Jong €75 million (£65m/$85m) move to Camp Nou.
And now a source from the Catalan club consulted by Goal confirmed the signing of the Netherlands international is very close to being completed, but nothing is official yet.
Barca hope to make the announcement in coming days, with Goal previously reporting the starting price for De Ligt ranged between €70-€75 million.
The 19-year-old defender has seen his stock continue to rise this season as he captained an Ajax side that pushed all the way to the Champions League semi-final.
The surprise run saw the Eredivisie club shock reigning champions Real Madrid and Juventus in the last-16 and quarter-final rounds, with De Ligt scoring the goal which sent Ajax through against the Serie A champions.
That run nearly continued to the final in Madrid, but a Lucas Moura goal deep in stoppage time saw Ajax eliminated in heartbreaking fashion against Tottenham.
De Ligt’s exit from Ajax is a foregone conclusion, with club CEO Edwin van der Sar admitting after their Champions League exit the teen was playing in his final games for the club and hoped the defender would go out on a high.
The CEO also said De Ligt would land in either Spain or England.
But Barca have now gained the edge on the competition, which has been rumoured to include the likes of Juventus, Liverpool and Manchester United.
Should they seal the deal, Barca will have made their second big signing away from Ajax this year, having secured the signature of De Jong, beating out the likes of Manchester City for midfielder.
Despite their Champions League heartbreak, the pair will exit Ajax having netted silverware in their final campaign.
Ajax won the KNVB Beker on May 5 with a 4-0 victory over Willem II and are set to complete the domestic double when the Eredivisie season comes to a close Wednesday.
The club hold a three-point edge over PSV heading into their finale against De Graafschap, but Ajax have a goal differential edge of 14 as a tie breaker, making the final matchday a formality.