The Romanian international is available from Spurs this month, who 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 as the new favourites to land Dragusin thanks to their willingness to negotiate an immediate, permanent transfer.
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