Van de Beek is yet to hit the ground running at Old Trafford, starting just two Premier League matches and three Champions League matches all season since his £40million transfer from Ajax over the summer.
The 23-year-old's latest appearance was a two-minute cameo in United's 2-0 semi-final defeat to Manchester City in the Carabao Cup - a competition where Van de Beek had started in every previous round.
Ajax legend de Boer, who works as a youth coach for the Dutch top-flight giants, claims the Dutch midfielder could seek a January exit from Ole Gunnar Solskjaer's side if his game time does not improve.d.
De Boer told Dutch news outlet AD: 'The European Championship is coming, he will undoubtedly want to be there. Maybe it would be good for him to discuss with the club exactly what they want with him.
'If the view on playing time does not improve, he may have to declare that he should be loaned or even sold.'
Van de Beek arrived in Manchester with a lot of promise after scoring ten goals and registering eleven assists for Ajax last season.
But the Dutchman has scored just once for Solskjaer's side - on his Premier League debut against Crystal Palace back in September - since his big-money move from Holland.
De Boer claims a potential reason why Van de Beek has yet to find his feet in England is due to his playing style - which is more suited to LaLiga in Spain, according to the Ajax youth coach.
He added: 'I think his playing style is better suited to the Spanish league than to the English.
'In the Premier League it is often hit and run, in Spain more combination football is played. Donny is physically fine. But he comes into his own better in the Ajax game.'
De Boer, however, does not believe that Van de Beek is a big-money Premier League flop and claims the young midfielder can turn his game around in Manchester.
He added: 'You have to be lucky every now and then. Of course it doesn't look great now, but with a great performance it can suddenly change completely.
'We also don't know what's going on behind the scenes. Perhaps they have made certain agreements with his transfer, they will get him ready for next year this season. That always remains a bit of a guess.'