Kicker claim Kent and Woodburn are two of the names being discussed for a season-long loan spell in the Bundesliga with the newly-promoted club.
Liverpool's loan pathways and football partnerships manager Julian Ward was spotted in Hannover last week, leading to suggestions that a player from the fringe of Jurgen Klopp's squad would be heading to Die Roten.
Hannover are looking for an attacking player - but early reports, informed by the club, made it clear that Divock Origi, Sheyi Ojo and Lazar Markovic were not under discussion.
Kent impressed in Liverpool's recent Audi Cup matches in Germany, particularly as a second-half substitute against Bayern Munich, where the 20-year-old is likely to have caught the eye of Hannover scouts.
Woodburn, 17, started in the Audi Cup final against Atletico Madrid and caused problems in the early stages, providing one superb cross from the left which should have been converted.
Both players could benefit from a season of playing regular football in Europe this year.