Both Premier League sides are watching the Ukrainian star, and Spurs got a glimpse up close last week when Konoplyanka's penalty proved to be the match-winner in their first-leg Europa League clash.
Liverpool were extremely close to sealing a deal to bring the Dnipro winger to Anfield during the January transfer window. But their late bid collapsed as the two clubs could not agree a fee.
Reds boss Brendan Rodgers is thought to be keen to resurrect the deal this summer, but Spurs are now sniffing around as well.
They were impressed by Konoplyanaka last week, and with summer signing Nacer Chadli out of favour under Tim Sherwood and Lewis Holtby out on loan, there is space for the Ukrainian in the Spurs squad.
The report claims Dnipro will be looking for at least £15m - the fee that was believed to be the figure discussed with Liverpool in January.
The 24-year-old winger was a target for Tottenham last month as well, and first came to Premier League clubs' attention after his stunning goal for Ukraine against England in World Cup qualifiers.