It is understood there is no break clause in the loan from Burnley, so talks would involve all three clubs.
However, the United boss knows he has to work under financial constraints following the summer outlay.
Weghorst arrived at Burnley with high expectations last January after a £12m move from German side Wolfsburg, but only scored twice as the Clarets were relegated to the Championship.
He returned to the attention of English audiences last month when he scored two late goals in the Netherlands’ epic World Cup quarter-final defeat by Argentina.
There have been a few names linked with Manchester United since Ronaldo’s exit.
Joao Felix was felt to be too expensive because of the huge loan fee and wages for the Atletico Madrid man.
Memphis Depay apparently wants a permanent move if he is to leave Barcelona.
Weghorst doesn’t match the other pair in terms of status, but he did score 70 goals in 144 games for Wolfsburg before he joined Burnley and he proved at the World Cup he still knows where the net is.
Ten Hag has faith in Anthony Martial as his first-choice number nine, but Weghorst offers a more direct option which could be handy off the bench.
Ten Hag did say United had to be creative. Signing his fellow countryman Weghorst would certainly be that.