The Romania international is available from Spurs this month, which are keen to sell in the coming weeks.
An attempt to take Dragusin on-loan by Roma has been rejected, with Spurs insisting on a straight sale.
Italian media sources say Leipzig have now stepped in and are ready to make a cash bid for the defender.
As it stands, Leipzig are regarded new favourites to land Dragusin thanks to their willingness to negotiate an immediate permanent transfer.