The Dnipro Dnipropetrovsk winger was heavily linked with the Reds in January, coming within hours of completing a deadline day switch to Anfield before the move fell through.
Spurs have since been watching the wide-man who starred against them in the Europa League, but United have also emerged as suitors.
New Old Trafford chief Louis van Gaal is thought to see the 24-year-old as a wise addition to his squad, as he looks to put the woeful performances of David Moyes’ time at the club in the past.
Konoplyanka is said to have a £12m release clause in his contract and would command relatively low wages, which again appeal to the Dutchman.
His signing would also allow Nani and Ashley Young to be shipped out, with the Eastern European able to play on either flank or just off of a main striker.
Dnipro are believed to be resigned to losing their star man this summer, despite putting up a fight in January to keep Liverpool’s interest at bay.
Brendan Rodgers may well look to make a fresh move, and is able to offer ‘Kono’ Champions League football.