United won 3-0 at Athletic Bilbao, who incidentally host the final on 21 May, while Tottenham saw off Bodo/Glimt 3-1 in London.
Statisticians Opta give United a 97% chance of reaching the final - with 91% for Spurs - meaning an 88% likelihood of both being there.
That would create just a sixth all-English final in any major European competition - with half of them involving Spurs.
It would also mean six English teams in next season's Champions League.