The Daily Echo says the 21-year-old, who will be playing for hosts Poland at the European Under-21 Championships this month, has already been subject of a 6m Euro offer from Saints.
If this offer were accepted it would make Bednarek the most expensive player in Polish top-flight history.
But despite the current bid testing Lech's resolve, they are currently believed to be in no rush to sell one of their most prized assets.
Hannover also holding a keen interest in the 6ft2in centre-back.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!