Former Germany U21 international
Leeds are desperate for a replacement for star striker Chris Wood after the New Zealand international made a £15m switch to Premier League side Burnley.
Lasogga will move to Elland Road for the remainder of this season and his parent club are willing to continue paying a portion of his wages as part of the deal, according to HSV24.
One of Lasogga's best moments in a Hamburg shirt came in October 2013 where he scored an eight-minute hat-trick away to 1.FC Nuremberg in a 5-0 victory.
Scoring Hamburg's second, third and fourth goals of the game, the German striker completed his hat-trick with a powerful 30-yard strike at the Max-Morlock-Stadion.
Lasogga will join compatriot Felix Wiedwald at Elland Road this season after the 27-year-old goalkeeper completed a £450k move from Werder Bremen earlier this summer.