Van de Beek scored a superbly taken right-foot volley early in the second half against Lyon at Murrayfield
The Dutchman, 26, has struggled to establish himself at Old Trafford since arriving for £35m in September 2020.
He had a loan spell at Everton in 2022 before returning to United, and missed the second half of last season with a serious knee injury.
"It is hard to say where my future is," Van de Beek said after capping his return from six months out with the winning goal in United's 1-0 victory over Lyon at Murrayfield in their second pre-season match.
"I am coming back from injury. I have trained for a few weeks now and I have played my first minutes today.
"I am fit but I still need to keep going and try to push as hard as possible. Let's see what happens. There is also the possibility that I move - everything is open."
Van de Beek's superbly taken right-foot volley early in the second half - arriving in the box to caress Daniel Gore's right-wing cross past Lyon substitute keeper Remy Riou into the left corner - was the highlight of a sunlit afternoon in the Scottish capital.
His roar of celebration hinted at his relief at ending a frustrating spell on the sidelines.
"For me personally it is a big moment," he said. "Of course it is nice if you score a goal, but people who have experienced such a big injury will know I have waited so long for this moment.
"I know it is only a friendly but it is a massive moment for me. You realise you enjoy football so much."
Van de Beek also welcomed the imminent arrival of his former Ajax team-mate Andre Onana, with United having agreed a £47.2m (55m euros) deal for the Inter Milan goalkeeper to replace the departed David de Gea.
"He is a great goalkeeper," the Dutchman added. "I played with him for many years and he is a great personality. He is good with his feet and good on the line.
"My expectations are high for Andre. He is a great person - I still speak with him sometimes - and a top-class goalkeeper."
While manager Erik ten Hag appears to have successfully landed one of his key summer targets, their afternoon outing in front of 48,484 fans in Edinburgh highlighted United's need for a new striker.
With Marcus Rashford and Anthony Martial not involved, the Red Devils started without a recognised frontman, Jadon Sancho taking up a central role, flanked by Antony and Amad Diallo in a front three.
The trio linked up well in the early stages but lacked a clinical edge as four chances went begging inside the first 10 minutes.
Antony saw a shot saved and Amad scuffed another effort wide, before the same player forced a fine save from Anthony Lopes with a stinging left-foot effort after Anthony's precise cross from the left.
Sancho might also have done better when he sprung through the middle but took too long to find the unattended Mason Mount in the box, the midfielder crowded out by the time the ball reached him.
Apart from goalkeeper Matej Kovar, Ten Hag changed his entire team for the second half, with Fred taking over the captain's armband from Raphael Varane and veteran centre-back Jonny Evans, signed on a short-term contract, making his second United debut.
The closest United came to adding to their lead came when Isak Hansen-Aaroen, an 18-year-old left-sided attacker, collected Fred's pass and cut on to his right foot but the Norwegian's curling effort was tipped round the far post.
The United squad will fly out later from Edinburgh to New York, where they begin their four-match US tour with a fixture against Arsenal in New Jersey on Saturday.
They have named a full-strength squad for the trip, with Harry Maguire included despite his future at the club being in doubt.
Cameroon goalkeeper Andre Onana is also due to join the squad when he has completed his move from Inter Milan.
Midfielder Fred will remain in the UK to deal with a personal issue and will link up with United at some point on their tour.
-- Courtesy of BBC Sport