Having received the green light from the Spaniard, the Partenopei are working towards finalising a deal with the La Liga outfit.
The Serie A champions are hoping to strike an agreement with Celta for around €36 million plus bonuses – which could take the figure close to his €40m release clause.
Veiga has been identified as a potential replacement for Piotr Zielinski, who is edging closer towards an exit from the Diego Maradona Stadium.
The Polish midfielder has declined an extension offer from the Partenopei, and Al-Ahli are on the verge of signing him.
Having already signed Riyad Mahrez, Allan Saint-Maximin, Edouard Mendy, Roberto Firmino, Franck Kessie and Roger Ibanez, Al-Ahli are close to adding Zielinksi and Atalanta defender Merih Demiral.
Veiga also courted interest from Borussia Dortmund, Real Madrid, Manchester City and Paris Saint-Germain, but none were ready to meet his release clause.
The 21-year enjoyed his breakout campaign last term, netting 11 goals and four assists in La Liga.
His best performance came against Barcelona in the final game of the season, as he scored a double to inspire Celta to a 2-1 win.
Veiga could become the third summer signing for the Neapolitans following the arrivals of Jens Cajuste and Natan.
Napoli have recently confirmed the contract extension of Mario Rui, who has penned a new deal to extend his stay until 2026.
Victor Osimhen could be next, as the Partenopei are reportedly closer towards finalising a new deal for the Nigerian striker.
Napoli will begin their title defence against newly promoted Frosinone on Saturday.
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