Wiese's contract expires in the summer and he has already informed Bremen that he will be leaving.
Although Wiese yesterday denied he had already agreed to join Hoffenheim, it is something Babbel would like to try and make happen.
"When Germany's number two is available on a free transfer and is on the market, then it is my duty to do all I can to complete a transfer and convince him that we play good football in Hoffenheim," he said on his club's website.
"He has a great deal of experience and has managed to play at a consistently high level, and he knows what it means to play in Europe too.
"I think he is an excellent goalkeeper."
Should Wiese arrive, he would probably replace fans' favourite Tom Starke between the posts and Babbel says he has already discussed such an eventuality with his vice-captain.
"He reacted very professionally," said Babbel. "That is just what I expected from him.
"One thing is clear - in professional football, you do have battles for places in every position and you have got to deal with that."
However, Babbel was keen to stress that a deal for Wiese to move south has not yet been complete.
"I expect a decision one way or another in the next few weeks," he said.
"No contracts have been signed and we have not even made him an offer either, but he is aware of our interest and we will sit down in the coming days and hope that he comes to us.
"But there are other clubs who have signalled an interest too."
Wiese said he was leaving Bremen to join a side who can challenge in the Champions League and many could see a move to Hoffenheim as a step down in his career.
However, Babbel still believes he can sell his project to the Germany number two and that, with his help, they can also challenge for a place in Europe's elite club competition.
"Of course the Champions League can become an issue around here too," he said.
"I am a hungry coach and I want success. To be able to achieve that, you need the suitable players and we are working on putting together a competitive squad."