The 25-year-old Ukraine international is set to be a free agent in the summer as his contract ticks towards its end, which has attracted Spurs.
Although Dnipro want to keep their man, selling this month rather than allowing Konoplyanka to run down is deal makes sense, with the Eastern European club keen to get some cash in for their star man.
They do, however, want £7m, and Man United, Everton, West Ham, Inter Milan and Monaco are also keen.
Yet, the player himself is thought to favour Spurs, which could allow Mauricio Pochettino to get his man.
Liverpool were linked with a £20m swoop for Konoplyanka just under 12 months ago, but they could not beat the January transfer deadline to seal a deal.