The former Werder Bremen stopper let in 11 goals in their first three league matches of the campaign before a groin injury kept him out of the next four games.
Markus Babbel's side conceded just three times during that period but the boss hinted that Wiese could replace Koen Casteels between the sticks.
"Tim Wiese has taken part in all of our training sessions and is looking very good," said Babbel.
"I expect him to be fit. So far, he has made a very good impression."
The 30-year-old would probably welcome a return against a side who have scored the fewest goals in the Bundesliga this season - just two - but Babbel has warned whoever is given the nod to expect a busy night.
"Furth are a team who have nothing to lose. They have been playing stronger away from home than at home and we are going to have to be very alert, " he added.
"It is an important game for us, there is no two ways about it. We had a bad start to the season and recently started a positive trend, but we have got to keep it up."
The Bundesliga's bottom side have amassed all their points away from home thanks to a win against Mainz and a draw in Wolfsburg and Furth coach Mike Buskens hope those results can inspire his side in Hoffenheim on Friday.
"We want to latch on to those games, as well as the first half in Leverkusen," he said at a press conference.
"We are coming up against a side who, after initial difficulties, have been picking up points lately and they would like to move on towards a place in Europe.
"We are going to have to defend well and take our chances."
Stephan Schrock left Furth in the summer to join Hoffenheim and he could face his former team on Friday.
"It was great working with Schrocki," said Buskens. "It was a real pleasure. His development here was also very positive."