The Dnipro Dnipropetrovsk star came within hours of completing a switch to the Premier League in January as the Liverpool attempted to take him to Anfield, yet their efforts ended in disappointment.
Since then the Reds have remained keen, while Spurs and Arsenal have also entered the running.
But United are thought to be at the front of the queue after sending scouts to assess the Eastern European star over the latter half of last season.
Although not new manager Louis van Gaal’s top target, Konoplyanka is very much on the Dutchman’s list as he looks to add guile and quality to the squad that failed so spectacularly under David Moyes last term.
‘Kono’ is available for £12m due to a release clause in his contract, and Dnipro – one of the richer sides in Ukrainian football – have already suggested that they will be unable to keep their 24-year-old star at the club if big teams come calling.
French heavyweights PSG are also in the battle, and could bid the necessary amount as they look to further enhance their talented squad.
Konoplyanka himself is said to be ready to join a top level European club this summer.