The Brazil forward has been strongly linked with a move to Paris St Germain, but Valverde brushed aside such talk.
He delivered his third goal in two matches in the exhibition tournament as Barcelona handed the English Premiership club their first defeat of the pre-season.
The Catalans controlled much of the first half, with Neymar and Messi having early attempts before De Gea pulled out a fine, one-handed save to deny Suarez.
Barca also rang the changes following their 2-1 win against Juventus. Antonio Valencia stumbled when trying to cut out a Messi through ball, with calls for a foul ignored as Neymar slotted home.
Messi came close in the 12th minute, his low effort sliding wide.
Unsurprisingly such widespread alterations took the sting out of the game, with Barcelona dominating possession without creating a clear-cut chance until Paco Alcacer fluffed his lines.
It was one-way traffic from that point as De Gea denied Neymar from close range but the United shot-stopper was helpless to stop the Brazil global just past the half-hour mark.
Barca's lead could have been greater at half-time if not for De Gea after the Spain worldwide pushed away Suarez's inventive and acrobatic strike three minutes before the break.
Both coaches rang the changes at halftime, with Valverde replacing 10 players - only leaving Cillessen in goal.
Anthony Martial, Andreas Pereira and Pogba all threatened, but Manchester United were unable to find an equalizer.
It's an interesting matchup, with the not-quite-invincible superteam in Barcelona looking to regain their footing a bit this season matched up against a returning giant in Manchester United, who look to be on a big upswing after several years of doldrums.