Enke infection still unidentified
Enke was picked by the Group Four leaders for the match against Azerbaijan, as well as the final two qualifiers against Russia and Finland in October, before falling ill.
Blood analysis at a Hamburg institute specialising in tropical diseases showed no infectious illness and the keeper could now return to individual training, Hanover said.
"For a final diagnosis to determine the therapy more tests from various experts are necessary," the club said in a statement.
It is still unknown whether Enke will be fit in time for the next Bundesliga match against Borussia Dortmund. He was replaced by Florian Fromlowitz in their 0-0 league draw against Werder Bremen on Sunday.
Bayer Leverkusen's Rene Adler stood in for Enke in Germany's 4-0 win over Azerbaijan on Wednesday.