Lamptey, 19, has been catching the eye with some stunning performances for Brighton in the Premier League.
And Florian Plettenberg of SPORT1 reveals that Bayern are willing to offer €15m for Lamptey.
That will not be enough for Brighton, who expect up to €25m for the England under-21 international.
Lamptey only moved to the Seagulls in January, joining from Chelsea on a three and a half year deal.
Lamptey is the same age as Dest and would rotate with first-choice right-back Benjamin Pavard.