Reports in Kicker suggests that United have been scouting the highly-rated centre-back in recent weeks.
The Turkey international has a contract with Bayer Leverkusen until the summer of 2018.
Toprak is also reportedly being watched by Bundesliga champions Bayern Munich.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.