The Spaniard has had a good campaign with the La Liga outfit this season, scoring 9 goals and providing 4 assists from 31 appearances in all competitions.
His form has caught the eye of many European clubs and AS claim that United are one of the teams interested in prising him away from Celta in the off-season.
The same outlet add that the youngster could end up in the Premier League this summer unless Real Madrid make a serious effort to land his signature.
Celta are more than happy to sell their prized asset for his current £35 million release clause.
Veiga likes to operate from the central or attacking midfield role. The 20-year-old has impressed with his work rate, concentration and ability to create chances.
He still has to work on his overall distribution but that should improve with experience. United are interested in him and they could make an approach this summer.
Bruno Fernandes is currently an undisputed choice for the number 10 role at United and there has been no competition whatsoever for the Portuguese this season.
Donny van de Beek has barely managed to impress since his transfer from Ajax three years ago and he is currently sidelined for the campaign with a knee injury.
Marcel Sabitzer recently got the nod in the role but the Austrian is not known for his intelligent passing in the final third. He was poor with his distribution at Sevilla.
Veiga could be seen as a potential understudy to Fernandes at United and the price tag seems reasonable for a player described as one of the best young Spanish stars.
United will be hoping that Madrid don’t enter the race. Carlo Ancelotti was recently full of praise for the youngster and said that he is a ‘good player‘ with quality.